If there weren't any operators, what would happen to nuclear power reactors?

If you saw the show"a day without humans"on the national geographic channel,they said,that eventually the power would shut off,which in turn would kick in the back-up generators,but then,like you said if there was a plague,there would be no one to refuel them causing the system to shut down and the reactor to reach critical m,overheat and explode.It was an interesting show,but it also was a "Bad humans" and humanity type vibe from the environmentalist point of view.(Typical of them)