Well, many private prisons have occupancy guarantees. In the Private Interest, an anti-privatization group, recently released a report studying occupancy guarantees. It identified 77 county and state-level private facilities nationwide and was able to collect/analyze the contracts of 62 of the facilities. 65% had quotas and they ranged from 80-100% (most at 90%). So it looks like in many cases, the government is paying the bill no matter what.
I found this map interesting:
