In a right to work state, you could indeed walk in, terminate your employment, and file a patent later. You could then charge that company for that work. In civil court, it would be argued as to when you actually had the idea.

In these civil suits, the one with the most money wins, so you would still lose even if you indeed solved the problem after you left.

No need to defend those huge corporations. They're perfectly capable of bribing officials to screw over employees all by themselves.