We know stories about people in the Soviet Union or in Germany where they were constantly trying to flee the borders/walls to get into the capitalist society. How often the inverse happened? Did communist countries were open to receive people willing to support the regime or they were closed to receive just like the way they were harsh to accept people leaving?
Robert Robinson is a pretty interesting example. He was a black autoworker at Ford who was offered a contract to come work in the Soviet Union in 1930 where they desperately needed skilled workers for their rapid industrialization. He re-upped his contract several times and earned a degree in mechanical engineering in Russia. After the war he was repeatedly denied an exit visa until 1974 when he was allowed to move to Uganda. Finally in 1980 he was able to move back to the United States. He offers a pretty nuanced account as he rose to heights professionally that he never would have been able to in the United States at that time while also having a front row seat to Stalin's purges and living through years of a different kind of oppression in the Soviet Union.
Here's a short newspaper blurb about his life: http://news.google.com/newspapers?id=wChUAAAAIBAJ&sjid=mo0DAAAAIBAJ&pg=6545%2C179684
and his autobiography is called "Black on Red: My 44 Years Inside the Soviet Union"
In the case of Germany this happened more often than one might think. However, there are two phases to be distinguished:
In the period from the end of WWII until the erection of the wall migration between the two German states was quite common. From 1950 till 1968 about half a million people moved from the western part of Germany into the areas of the Soviet occupation zone. One of the most famous examples is the family of today's chancellor Angela Merkel who was born in Hamburg and moved to Brandenburg in 1954. Most of these migrations are assumed to be job- or family-related. Merkel's father, for example, got a pastorate in a Brandenburg village.
After the erection of the wall, things changes drastically. From 1964 to 1984 only 48.000 persons immigrated to the GDR from western Germany, a considerable amount of them with a more or less vivid political motivation. In this period immigration was also aggravated by the East German government's fear of western spys, which is why immigrants were interned for a few months or so until they were allowed to enter.
If you are interested in further reading and able to read German, I recommend this book by Andrea Schmelz.
It depends upon the time and the place. It's worth keeping in mind that Communism was mainly successful in the developing world. The only industrialized countries that really became Communist were West Germany and Czechoslovakia (both of which long remained the most developed Communist countries until the fall of Communism, even as they lagged behind their capitalist neighbors). You don't really need the specter of a Communist dictatorship to dissuade a person living in a developed country from immigrating to a non-developed one - immigration in that direction is always going to be relatively rare. As well, the Communist countries weren't necessarily a unified bloc, and their approaches to immigration varied in different countries.
In any case, there was the famous case of 21 American POW's who refused to return after the Korean war, along with 6 who crossed the DMZ after the war. This sparked concerns about brainwashing, and contributed to the abuses found in the infamous MK-ULTRA experiments. There were also 327 South Koreans who defected. Defecting as a South Korean would make a great deal more sense than defecting as an American - America is, of course, a rich, developed country, while South Korea, at the time, was less developed than the North and was an oppressive military dictatorship itself. Even given that, there were far more defections the other way around - tens of thousands of North Koreans refused repatriation to North Korea. But North Korea, generally, isn't accepting of immigrants. You and I would be hard pressed to wander into North Korea and peaceably approach whatever immigration offices they have to submit an application. Soldiers who defect hold propaganda value, though.
As for the Soviet Union, there were fairly strict immigration laws even early in it's existence. Thousands of idealistic westerners sent applications to the Soviet Union in hopes of seeing a "socialist state" in action, but most were denied. In the Great Depression, there was actually a great deal of illegal immigration to the Soviet Union, due to the fact that it was one of the few countries that maintained relatively steady and swift growth during that period. But mostly it was shut down as Stalinism became ever and ever more severe. There was, however, the curious case of Lee Harvey Oswald. Before he murdered the president, he was an ex-marine who wandered into the USSR under tourism pretexts, and defected once inside - the authorities there honestly didn't know what to do with them at first, it wasn't a common occurance, but, again, a defecting former Marine has propaganda value, so they found a place with him. Rather predictably, he became bored with the place after a couple of years, and emigrated back to the US (he still had his US citizenship, as his renunciation was done according to the strict means usually required - countries don't make it easy to renounce without having taking up another citizenship, in order to avoid the headaches of dealing with the stateless).
The last big case I happen to know of, is that there were a few westerners, such as Sidney Rittenberg, who helped out during the early days of the Chinese Communist party, and decided to stay on, and were granted citizenship. Most of these people suffered abuse from Red Guards during the fanaticism of the Cultural Revolution, however - as a strange, foreign element in a society with few foreigners, they were always suspect.
I was waiting for primary responses to be filled in so that I could add my snippet. I haven't seen mention of Zainnichi Korean repatriation yet.
Korea and Japan have been intertwined for thousands of years. Many ethnic Koreans exist in, and have fully integrated into Japanese society (names, intermarriage), yet they still face segregation and discrimination because of Japan's racially closed society. Their population is one or two million people. Zainichi faced extremely difficult circumstances in Japanese society. Many desired to keep their heritage alive, while others opted to hide their origins and integrate. Famously, the yakuza of Japan recruit and are often founded by Zainichi Koreans.
In the late 1960s, Japanese Communist Party leaders and Zainichi Korean intellectuals called for Zainichi to return to 'humane' North Korea. [added sentence for context] This was a kind of 'return to the homeland' type movement, not a 'get out of Japan' type movement. Many did so. A return to 'Chosen' was seen as valid response to this less than desirable status in Japan. More than 90,000 Zainichi Koreans moved from Japan to North Korea. Oddly, many, if not most of these people, were actually of Southern Korean origin. The Japanese government, and by proxy, the U.S. government, were happy to be rid of communists and Zainichi -- both seen as a threat.
More than 100 of these self-repatriated individuals later escaped from North Korea. As we now know (they didn't at the time), North Korea is not a nice place. What's more, when they arrived, they faced discrimination as 'Japanese'.
Sources:
Just like those that fled communism were a diplomatic coup for capitalist countries, the same was true for communist countries.
"Hi world, as wonderful as those free enterprise countries are, why are some of their citizens leaving for communist havens?"
As someone else pointed out, there is the documentary on Netflix about the couple of American defectors to North Korea.
Also, both Cuba and the Soviet Union capitalized on problems in American with race relations during the Cold War. African American actor Paul Robeson made several trips to the Soviet Union to publicly show how he was not discriminated on the basis of race there. He did not immigrate there, but did make several trips and the Soviets were more than happy to likewise use him to depict the unequal treatment of people in the US.
An African American named Robert Williams did immigrate to Cuba and was very much welcomed. He left the US following some trumped up charges of kidnapping during one of the Freedom Rides. Not only did they welcome him, the Cubans actually gave him access to a radio station to broadcast to southern Florida (I don't think it reached much further). There is an interesting book about Williams' story called Radio Free Dixie.
The Soviet Union had a bit of attraction to black Americans and citizens of newly independent African nations, due to the purported anti-racist social policy. There are estimated to be roughly 40,000 Russians of African/black descent today. source 1 source 2
The Soviet Union utilized this for various geopolitical reasons. For example, it established a Patrice Lumumba University, which specifically was created as an educational destination for individuals from the Third World. Here is the university's website and history page.
An earlier, prominent narrative is Langston Hughes and other poets/filmakers traveling to the Soviet Union in the 30s to make a film depicting the American "negro condition". They eventually got the shaft, though, because Moscow was trying to establish an embassy in DC and had to tone down the racial struggle overtones. Arthur Koestler writes about this in his autobiography.
It is difficult to say how many people initially moved to the Soviet Union to escape racial discrimination. In the second link, an Afro-Russian provides an anecdote, which, and I realize this isn't the greatest source, seems to mesh with a few anecdotes I've heard from Soviet Union/Russian emigres I know personally. Basically, Afro-Russians are frequently the only black individuals in their given town - they are treated with anything from curiosity to hostility. After the Soviet Union fell, racism and xenophobia became much more prominent. An estimated ~100 people are killed per year in racist attacks, although these are primarily focused on Central Asians.
Very surprised to see no mention of Lee Harvey Oswald, who defected to the Soviet Union in October 1959 when he was about twenty. As soon as he arrived he would declare his intention to defect to almost anyone he encountered, including his tour guide. When asked by officials why he wanted to become a citizen, he could only declare himself a communist and give vague responses about how amazing the Soviet Union was.
Even though he was a former radar operator the USSR denied his citizenship application and he tried to kill himself after they told him he had to leave. He was re-interviewed by Soviet officials who decided he could stay. He then went to the US embassy in Moscow and told them of his intentions, and his plans to give up any secrets his job had given him access to.
The Soviets assigned him a job in a factory in Minsk, and he eventually met, married, and had a child with a Russian woman. He grew disillusioned with his job and the effects the regime had on his social life, so he wrote the embassy and asked if it was okay to comeback since he hadn't formally renounced his citizenship. Not only did they allow him back in the country, he was allowed to bring his Russian wife and child along with him. The embassy even loaned him almost $500 to repatriate, and in the summer of 1962 they made their way to the US.
The manner in which he left (which was covered by news outlets in America) and the even stranger way he was allowed to re-enter the US are two things conspiracy theorists love to use as "proof" there was more going on there than meets the eye. I am not familiar enough with cold war era defections and the laws involved to make comment on whether his case was an abnormal one or not, but would welcome anyone who does have such knowledge to comment on the situation.
Nikolay Ezhov's biography [1] mentions that in the period of 1921—1936 some 58000 people have illegally passed the borders of Byelorussian SSR, mainly from Poland.
In the period of 1930—1934 between 10000 and 15000 have moved into Karelia region, more than 6000 of them from USA and Canada. (Most of them were of Finnish origin.) [2]
Some also moved from Romania to Soviet-controlled Bessarabia (Moldovan SSR). People of Eastern-European Jewish origin were moving to Jewish Autonomous Oblast of Russian SFSR. I don't have numbers for those.
[1] Павлюков А.Е. Ежов: Биография. М.: Захаров, 2007. 574 с. 5000 экз. Also, on http://www.hoover.org/publications/books/8348
[2] Такала И.Р. Финны в России: история диаспоры // Россия и Финляндия: проблемы взаимопонимания XVII - XX вв. М. 2006, с 246
Actually, this happened to a substantial subset of the Finnish American population. Towards the close of the 19th and the opening of the 20th, there was a lot of migration Finnish areas (what we today call Finland, but also Karelia in Russia) to the US. This was as often politically motivated against socialists as it was a search for wealth, opportunity, and a certain strain of utopianism. The Finnish people who did arrive often formed a major contingent of American socialist organizations. However, at the creation of the Soviet Union, many returned to Karelia to help with sovietization. It did not go well for them.
Wikipedia has a quick link, there are a few books on the matter, but here a quick little link about it from a more reputable source on the matter: http://www.sras.org/finnish-americans_in_the_soviet_union
There are quite a few people who defected from the 'West' to Russia or other Eastern Block states. Perhaps most famously, assassin Lee Harvey Oswald, who renounced his U.S. citizenship in 1959 and lived in the U.S.S.R., primarily Minsk until 1962. While in Minsk, Oswald met and married Marina Prusakova, who returned with him to the United States. Additionally, while it is a little murky, it appears as if Oswald again attempted to defect to Cuba or possibly the Soviet Union via their embassies in Mexico City in 1963, shortly before his big moment in history. (Warren Commission).
Another historical example of westerners defecting to the Soviet Union included members of the British spy ring known as the Cambridge 5, which included highly placed British intelligence and foreign service officers Donald Maclean, Guy Burgess, Harold "Kim" Philby and Anthony Blunt, with the possible 5th member of the ring still unidentified. Three of the four defected successfully to the Soviet Union after their activities had been discovered. Burgess and Maclean defected in 1951 while Philby fled to Russia in 1963.
While in Russia, Philby got a monthly stipend and little else and was closely monitored by the KGB (The private life of Kim Philby, the Moscow years -Philby, Rufina & Peake) and according to the New York Times, drank heavily and attempted suicide. Maclean did pretty well for himself in Russia, teaching English and serving in a variety of international relations roles, primarily as a specialist on Britain. I'm afraid I don't have much to offer on Burgess beyond the fact that he died in Moscow in '64.
Thousands of Americans emigrated to the USSR in the 1920s, when America was experiencing the Great Depression and the USSR was experiencing rapid growth as it industrialised. Many of them worked in the Ford-affiliated plant in Gorky referred to above. This was during the period of uneasy peaceful coexistence between the USSR and America between the Russian Civil War and the Molotov-Ribbentrop Pact.
While some of the emigrants had planned to return to America after a few years, in some cases they were barred from leaving the country. The American state department generally didn't intervene strongly on their behalf since they were viewed with suspicion as likely communists. Ultimately, some of them were killed during the Great Purges of the 1930s.
Most of the refugees who were escaping to Communism were also escaping from Communism.
In 1994, UN High Commisioner for Refugees published an article on foreign refugees in the former USSR. It said:
"In 1994, UNHCR knew of over 60,000 people in Russia from outside the CIS and Baltic states who were claiming to be refugees. Almost half of them came from Afghanistan, the other large groups being from Somalia, Iraq, Sri Lanka, Angola, China, Ethiopia and Zaire. The number of illegal migrants, many of them in transit westward, is believed to be considerably higher, perhaps as much as half a million. An estimated 150,000 Chinese alone are believed to have entered Russia illegally." - (http://www.unhcr.org/3b540eae4.html)
A large number of refugees, about 100,000, came from China to Khazakhstan during the Cultural Revolution. Most of these refugees arrived between 1966 and 1969. (http://books.google.com/books?id=KHUYRM2527sC&pg=PA315&lpg=PA315&dq=%22cultural+revolution%22+AND+refugees+AND+USSR&source=bl&ots=DRp3oD6v5q&sig=YhPw9LDMpZJZZL9lXocK7E4DBKM&hl=en&sa=X&ei=27P6UoTNM-mR0QG014DQAg&ved=0CD4Q6AEwAw#v=onepage&q=%22cultural%20revolution%22%20AND%20refugees%20AND%20USSR&f=false)
John Peet, my grandfathers cousin, worked as a reporter for Reuters and defected to East Berlin in 1950, having been a communist for most of his adult life, prior to which he fought in Spain as part of the International Brigade. I think it caused a bit of a stir at the time, and he spent a good part of his time there up until his death in 1988 writing for a periodical circulated in the West which sought to debunk some of the myths circulating about the GDR after it's foundation. If you can find a copy, his autobiography makes for a facinating read.
http://en.wikipedia.org/wiki/John_Peet_(1915%E2%80%9388)
(Edit: To further answer your question, it appears that he was able to do so easily after making contact with friends in the Soviet zone, and was pretty much able to simply walk across due to the lack of the Berlin Wall at that point)
When the civil war in Greece ended in 1949 with a defeat for the communists, about 100,000 fighters, sympathizers and also people from evacuated areas fled to the socialist countries through Yugoslavia and Albania and settled in the USSR and the Eastern Block countries. Most of them were not allowed to return to Greece until the 1980s.
Wikipedia has an extended article on this.