I've dealt with a lot of situations where I was the agent offering the Cash for Keys- it all varies from bank to bank, on amounts, time frame, etc- or if they offer it at all. To answer the other part of your question, I have never had a bank say that the occupant can rent until the house sells- what would prevent the occupant from not allowing the house to be shown in that circumstance?
If I were in your shoes, I would start making plans, assume that your options are just as they are today- that way, if CFK is offered, it isn't something you are counting on. I recently oversaw an eviction where the occupant had rejected CFK as too small, couldn't cover his expenses, etc- and his wife was watching tv when the crew of 9 men, and the sheriff, showed up and legally began to pile her household goods onto the lawn. That was NOT a good situation, and I'd hate for any family to have to go through that.
so sorry that you find yourself with this situation.
Krisan in KC