"Taking into consideration the gravity of the charge leveled against the accused, namely that he personally supervised the killing of more than 30,000 men, women and children, and considering the extreme display of cruelty which the subject showed when carrying out his tasks, the accused is hereby sentenced to death. Accused was executed by those who can never forget, on the 23rd of February, 1965."

- Note left on the mangled corpse of Herberts Cukurs, Nazi collaborator. Sao Paulo, Brazil. February 1965

As you correctly noted, most of the pertinent information is classified and has been obscured over time (either simply because primary sources are so scant or because of the "underground" nature of this subject in the first place), so it is difficult to conduct as robust of a historical analysis on it as we can for other WWII topics. However, there is indeed some evidence that Nazis were subject to extrajudicial pursuit and assassinations after the war. I will divide my comment into two sections - killings conducted by vigilantes, and those conducted by state actors (most notably the Mossad).

Part I: Vigilantes.

First of all, vigilante justice was extremely common in the closing days of the war. In Czechoslovakia, 500-1000 surrendered Wehrmacht soldiers and their families were burned alive by Czech nationalists in an event known as the Czech Hell. Nazi collaborators were also subject to mob anger. In Yugoslavia, the Allies refused to allow Croatian collaborators to escape the country; instead they were handed to the Yugoslav partisans who began them on a brutal forced march, interspersed with mass executions and general ill treatment. This is known as the Bleiburg Tragedy. The number of prisoners killed ranges from 13,000-70,000. In France, there was similar vigilante justice across the country. Most historians accept there were around ~4,000 lynchings after liberation.

There were also vigilante groups formed by Jews who had survived the Holocaust - while most able bodied Jewish men and women put their energy into rebuilding or going to assist the war effort in Israel, some Jews instead opted to focus on enacting revenge upon their former oppressors. There was a feeling that the Nuremberg trials (and the smaller associated ones) did not even come close to achieving justice for the victims. A few Jewish volunteers decided therefore to take matters into their own hands. The most notable of these groups are are Nakam and Tilhas Tizig Gesheften. Nakam is mainly known for its attempts at mass poisoning; as sympathetic as their background might be, it was by all reasonable definitions a terrorist group. Initially there was a plan to poison the water supply of the entire city of Nuremberg, as the Nakam leaders believed every man woman and child in Germany should pay in blood for the Shoah. But this was discovered and collapsed due to logistical issues. The plan was then refined to poisoning bread being shipped to a prison that was holding SS personnel prior to their trials. The goal was to poison the entire camp, and the tainted bread indeed make its way into the prisoners' rations - however, despite 2,283 thousand prisoners becoming acutely sick in that time period and 207 being hospitalized in critical condition, there are not very good records kept on how many died from this specifically.

Tilhas Tizig Gesheften was separate Jewish group that opted for more "man-to-man" style summary punishment. It was led by Israel Carmi, an associate of other underground partisan units such as the Jewish Brigade and the Haganah. Carmi and his volunteers operated in Germany, Austria and Italy, focusing on identifying former Nazi-aligned officials they believed had a hand in orchestrating the Holocaust. The modus operandi was to go to the house of a Gestapo official and shake him down for names and lists of his associates. Then Carmi would evaluate each name on the list. After being convinced of an individual's guilt, they would kidnap that person - either a direct abduction from his house or pretending to be Allied interrogators taking him to a police station for questioning. They would drive into an isolated area such as the woods, briefly present him with the accusation and conduct an unofficial trial, followed by hanging or a bullet to the brain. TTG operated only for a short time as Carmi was recalled to Palestine to aid in emigration of Jews from Europe. Exact dates, numbers and places of its operations are difficult to come by because surviving TTG operatives have been extremely reluctant to divulge specific information during interviews. Roughly, it is estimated that a few hundred Gestapo and SS personnel met their ends in this way.

Part II: State Actors.

Again, take all of this with a grain of salt because even the most rigid historical scholarship on the subject is limited by classified documentation and the muddy nature of clandestine operations. Briefly, I will focus on Mossad actions in the decades after WWII. The most notable of these is of course, the capture of Adolf Eichmann and his eventual execution in Israel; however this could be argued as legal since he was given a lengthy public trial. Beyond this, a few Nazis are known or suspected to have been assassinated by either Mossad agents directly or people funded by the group. Aleksander Laak was commandant of the Jagala concentration camp in Estonia. He is linked to at least 10,000 deaths of Jews within the camp. After the war he fled to Canada. In 1960 he was recognized as a participant in the Holocaust, and before a proper trial or extradition attempt could occur, he was found hanging from a wooden beam in his garage. Initially the official analysis was that he had committed suicide; however, recent scholarship has made a case that he was actually tracked down by Mossad-assisted operatives, confronted with his crimes, and given the choice of execution or suicide.

Herberts Cukurs was a Latvian Nazi collaborator who was a member of the Arajs Commando, a unit which mass murdered Jews in such famous events as the Rumbula Massacre. He was particularly notable for being cruel even among the group of collaborators; there are stories of him locking Jews inside the local synagogue before burning them alive within it while satirically playing traditional Jewish music on the loudspeaker outside. For this he received the moniker Butcher of Riga. After the war he escaped to Brazil. In 1965, the Mossad tracked him down and sent agents to deal with him; they lured him to Uruguay under the pretense of starting an aviation business, as he was an avid flyer. When he arrived at the safe house, he was confronted with his crimes and executed with two shots to the head. His body was found in a trunk the next week. A note was left on his corpse, the quote at the beginning of my comment.

Beyond this, we cannot really say which post-war Nazi deaths were the results of accidents or covert assassinations. Theories certainly abound when it comes to specific cases - Gustav Wagner for example was a particularly notorious SS overseer at Sobibor concentration camp, who managed to escape the war and hide in South America. In 1980, shortly after his identity was made public, he was found with a knife in his chest. The official documentation is that it was a suicide, although he left no note and never really displayed any guilt prior. But since there is no evidence to the contrary, any alternative narratives are just speculation. There are several of these cases sprinkled throughout the historical record - given the scarcity of available sources here, these will likely forever remain a mystery.

---

Sources:

Angrick, Angrej, and Klein, Peter, The "Final Solution" in Riga: Exploitation and Annihilation, 1941-1944, Berghahn Books, 2009

Fritz, Stephen (2004). Endkampf: Soldiers, Civilians, and the Death of the Third Reich. Lexington: University Press of Kentucky

Gay, Ruth (2008). Safe Among the Germans: Liberated Jews After World War II. New Haven: Yale University Press

Kimche, Jon; Kimche, David (1995). The Secret Roads: the "Illegal" Migration of a People, 1938 to 1948

Pavlowitch, Stevan K. (2008). Hitler's New Disorder: The Second World War in Yugoslavia. New York: Columbia University Press

Wyman, Mark (1998). DPs: Europe's Displaced Persons, 1945-1951. Cornell University Press

I want to present a case that happened around the Austrian village called Bleiburg, which some will immediately recognize and ask: Does this qualify as an answer if the question revolves around German Nazis?

And the answer would be: Not entirely, as the question is politically charged, especially, as always, in former Yugoslavia. Therefore one should ask whether members of the Ustaša and Domobrani and other fascist militant groups should be thrown all in one pot. This does not represent my opinion, but should moreso reflect on how who was a fascist/nazi is still a hot topic of discussion. Fact is some German Nazis did die in the massacres around Bleiburg, thus why I mention it. Also the Ustaša did collaborate with the Third Reich and there are enough instances in works of historians where the NDH (the Independent State of Croatia) is called a puppet state of the Third Reich.

What happened?

After Germany's surrender on 8th May, then Ustaša leader Ante Pavelić ordered troops under his command to continue fighting the partisans but at the same time move northwards to Austria. The plan was to surrender to allied-controlled Austria under the British, because either they expected more humane trials or a chance to fight in later conflicts against the Soviet Union and especially Socialist Yugoslavia. But due to certain agreements with the Soviet Union the British were unable to accept their surrender. Ustaša negotiators were then handed over to Yugoslav officers in British headquarters and forced to surrender within an hour. To cut it short some hundred thousand refugees were fleeing the partisans and had nowhere to go and as expected war crimes followed, as fast as on Austrian territory in the fields of Bleiburg thus its name "the massacre of Bleiburg", "the tragedy of Bleiburg" and others. The victims were subjected to different forms of torture, for example death marches to inner Croatia or Serbia or mutilation and a lot of shootings of which only a few were put before a trial prior to their shootings. The number of victims is being disputed a lot, guesses range from a few thousands to half a million. Concerning German Nazis it may have been just a few hundres but I couldnt find mentions right now of discussiong their number. Overall the what happened can be described extrajudicial but with a semi-state-y tone to it. Concerning the number of victims is something that shapes the politics around commemoration although some victims and warcriminals are still alive. But historians seemed to have found a consensus of about 70'000 dead of probably 200'000 who tried entering Austria. Not all of them were in any form "Nazis", but as mentioned it is a hot topic. How to commemorate this event, who attends the commemoration, do you commemorate collaborateurs with the Third Reich and everything else around the ideologically charged questions also concerning post-Yugoslavia is better discussed in the second source I mention, an essay of Pål Kolstø. For a more detailed history on what happened exactly I'll recommend the first source I'll put below this answer. It is unfortunately in German, but represents the first German work on contextualizing the tragedy in its whole. If possible I will look for English ones as well, but I am unsure about how much this tragedy has been picked up by English-writing historians.

-Rulitz, Florian Thomas: Die Tragödie von Bleiburg und Viktring. Partisanengewalt in Kärnten am Beispiel der antikommunistischen Flüchtlinge im Mai 1945. Klagenfurt 2011.

-Kolstø, Pål: Bleiburg: The Creation of a National Martyrology. In: Europe-Asia Studies, Vol. 62, No. 7, The Yugoslav Communist Legacy (September 2010), pp. 1153-1174. Published by: Taylor & Francis, Ltd.https://www.jstor.org/stable/20787618. Last access: 31-05-2019 16:11 UTC.