I'd say "going to jail." I'd never use jailhouse. Rich people could get themselves transferred to a better, big-name hospital. It really depends on the treatment need and the area -- here on the East Coast, big-name hospitals are thick on the ground, whereas in most of the rest of the country, the states are so large and sparsely populated that it would mean a fairly long trip to the states good hospital. However, if the person was REALLY rich, they could maybe afford a private ambulance-type plane with private nurses, etc.

It's hard to answer general questions about America without knowing the region -- it's a big country!