Viktor Korchnoi became a man without a country.
It wasn't a political statement. Korchnoi wasn't a dissident. He just wanted to play chess. And, apparently, playing chess for no country at all was better than playing chess for the Soviet Union.
Let's set the stage. Since the Soviets dominated chess, they pretty much got to pick who would face off for the world championship. And pick they did, colluding to present favorable match-ups for their preferred candidates. And, for whatever reason (his Jewishness obviously played a role), Korchnoi wasn't preferred.
So Korchnoi defected. His plan was to go to the Netherlands, but they would not grant his citizenship. He ended up in Switzerland, but the naturalization took a while. This meant that when Korchnoi finally got his chance at the world championship in 1978, he represented... no one.
There is no happy ending here, at least short-term. Korchnoi lost both his chances at the championship, and had to settle for the title of the greatest chess player never to wear the crown. Long-term, however, Korchnoi stayed active into his 80s, and recently even became Swiss national champion. Meanwhile, most of his contemporaries have departed, be it chess or life.
Who knows, maybe being a man without a country had its benefits...