If you want a semi-historical platform to launch this hypothetical scenario from, Rudolf Hess would be a good example. He was imprisoned, along with other nazis, in a prison in West Berlin shortly after WWII. It was agreed that the different allied powers would take turns guarding this prison as long as prisoners remained. Fast-forward to the Cold War era, and that agreement had an unintended consequence: it gave the USSR a precious foothold in West Berlin. Thus, they vetoed every request for Rudolf Hess's release, until he died in 1987. He had been the lone inmate of the 600-cell prison for more than 20 years.

Now for an alternative history twist: the Cold War never ends, and Rudolf Hess is kept alive as a brain in a vat for thousands of years, with the Russians and the Americans continuing to take turns guarding him so that both sides can cling to that sliver of West Berlin.