Dynamo Berlin, a team affiliated with Stasi chief Erich Mielke, won ten straight East German championships thanks in no small part to blatant fixing by league officials.
Did this happen in other Soviet and Eastern European football (or hockey) leagues, or just East Germany?
In a sense. The CSKA hockey team, for example, was run by the Red Army, and functioned as an active-duty military unit. Because the Soviet Union had compulsory military service, this meant the Army could simply draft into service the best young players and assign them to play hockey.
The other advantage of this was that CSKA's players were technically soldiers, not professional athletes, which meant they maintained their amateur status for competitions like the Olympics, which didn't allow professionals to compete until 1998. The Soviet national team wasn't just made up of CSKA players, it was CSKA.
Did it work? In the 46-year history of the Soviet hockey league, CSKA won 32 championships. Between 1956 and 1988, the last year the Soviet Union competed, they won medals in every Olympics -- 7 golds, 2 silvers, 3 bronze.
This doesn't speak to other sports, but in the case of hockey, CSKA didn't need to fix matches because their structure and personnel had already tilted the competition in their favor.
It didn't hurt that CSKA also had Anatoli Tarasov as coach and architect of Soviet hockey. Tarasov was one of the most brilliant tactical innovators the sport has ever known, reimagining the game as one of constant flowing motion, diagonal movement, fluid passing, and exploitation of space -- all ideas taken from his earlier career as a football player and coach.
To paraphrase his philosophy: "In Canada it is the man with the puck who masterminds the pass, but among Soviet players, it is the man without the puck. This means in Canada, four men depend on one, while in Soviet hockey, one man depends on four."
Would the Soviets have dominated the Olympics if NHL players were allowed to compete? Obviously we can't answer that question, but there is this: between 1975 and 1991, CSKA played 36 games against NHL teams and won 26 of them.
Today's NHL plays a game much closer to Tarasov's version than the frankly thuggish style of NHL hockey that dominated the '70s and earlier.
A great question! Robert Edelman addresses this question in regards to football teams in the U.S.S.R. in his book Spartak Moscow: A History of the People's Team in the Workers State [(relevant pages 269-70)] (https://books.google.com/books?id=SKw1XTpiqMIC&pg=PA270&lpg=PA270&dq=spartak+moscow+rigged+games&source=bl&ots=Fya2hn0v43&sig=_sMK914FfYnfkBbFnDDB3GtHOzg&hl=en&sa=X&ved=0ahUKEwjSmcTv2tDJAhUHWSYKHYq6AT4Q6AEIGjAA#v=onepage&q=spartak%20moscow%20rigged%20games&f=false). His assertion is: yes, sometimes, although less frequently than you might think in the case of Spartak Moscow, and generally difficult or impossible to prove.