I think the question you're asking is, if you go into foreclosure, what risks are there beyond losing the house, which is underwater and you don't want anyway? Your dad's credit will take a hit, and he would be liable to the bank for the difference between what they eventually sell it for at auction, and what was owed on the loan. He would probably be sued for that, plus all kinds of additional fees and penalties. That takes a long time to play out, but could end up being a lot more expensive than selling the house yourselves and dealing with the shortfall.
A friend of mine lived in a place, paid rent reliably for years, and the landlord defaulted on the loan. He collected rent for four years after he stopped paying the mortgage. Sounds insane but sometimes these things take a long time to resolve.
A short sale may be a better alternative. Have you considered doing a short sale with the bank?
