You legally could--if a bank were willing to do this--refinance under the same terms: that your parents (in this case, your father) could live there for the rest of his life if he chose. Whether he wants to or will do so is irrelevant: he has a legally binding right to live there, and you cannot take that right away. So to refinance, you'd have to incorporate that exact same right. But a bank might be unwilling to do that, because 1) it is very unusual, and banks are conservative--they don't like anything new or different; and 2) they may not like having another person having a legal right to reside in the home, since that muddies the water--it's no longer just about them and you (the people giving and taking out the mortgage), but rather there is a 3rd party (your father) involved. So a bank could choose to say "no," which is their right; there is no right to a mortgage or refinancing, and the bank gets to choose who they will lend to or refinance.