I can't speak about USSR but in Czechoslovakia there were many ''professional'' athletes and sportsmen , for example hokey players or even some soccer players. Problem is that the government didn't officialy approve something like this. They had to go to work or at least fake that they are going to work because everybody had to be working. In many cases officials closed eyes so they could easily practice during working week. The rewards for winning competitions weren't as big as in the west but they could live from it. There are players (hockey) who emigrated during they time abroad for example Peter Stastny. His sons play hockey now for USA national team.

I'm more familiar with the hockey aspect of it, and will go from the Soviet Union perspective. In the 70s and 80s players were given a bit better accommodation in terms of nicer apartments, and a little extra salary, as well as being pushed to the front of the waitlist for vehicles, but that was about it. Overall it was better than the common Soviet citizen, but by no means were the players wealthy. In fact during the 80s things changed even more (at least for the national team): under coach Viktor Tikhonov the players were largely confined to military barracks for 11 months of the year, forced to train and play hockey and only allowed free time for that one month. Tikhonov was an exception, though, a real hardlined coach who most players resented and was criticized by those who played under him, though after they had been able to either defect or once he no longer was in control. This is obviously in stark contrast to the athletes of professional sports in North America, who by that point were making considerable money and had much more freedoms.