Yes, it's a thing. Most of the deep space probes were radio-nucleotide powered. Earth orbiting is less common for obvious reasons. One option is boost to a parking orbit where it'll be stable and out of the way for a couple of thousand years. But the stuff from the '60s was often "it'll burn up on reentry (cross fingers) and it's a cost of doing Cold War business if a little get's scattered around".
There are plenty of earth orbiting actual fission reactors, not like the RTGs you have heard about.
There were quite a few sent up by the Soviets (from 1967-1988) and at least one malfunctioned, failed to eject its reactor into a disposal orbit and scattered radioactive waste across northern Canada.
Even the Soviets didn't intend to send nuclear reactors to burn up on reentry; I'd be surprised if that was anyone's plan.
I've more than "heard about" RTGs, and I'm well aware of the kind of reactors that have been shot into space. We can argue the level of "intend", but in the Cold War, the reentry of a nuclear reactor was considered an acceptable cost of doing business.
