I know the power the plant generates, it all goes to the grid, none of it goes back to the plant itself, the plant takes power from the grid to run although there are diesel generators and battery backups to boot up the plant to get it running from a cold start and/or to run it in an emergency. We have Shippingport here, Beaver Valley 1 and 2, and next to the atomic plant, there is a huge coal fired one so I'm sure they can get power from that.
The big thing is that if there is no operators, most likely the plant will scram and shut down, the control rod will be lowered as well as cooling water to cool the atomic pile down. IIRC, as long as the control rods remain in place, the reactor should just sit there until years and years of decay come in, provided there is no human intervention, where the containment building will start to fall apart and releasing radiation. I think it would take years and years, maybe a couple of hundred at least.