If the house is not in your name, it is not your house even if you were to pay it off, it would not belong to you unless he left it to you in his will. Remember girlfriends do not inherit anything unless it's in a will. Therefore, unless the house is willed to you, there'd be no point in paying for it, since you'd never end up owning it.If it will willed to you, you don't have to take it--you have the option of accepting the bequest, but also could refuse it you can't be forced to inherit. If you accept the house in this case, if you did not pay off the finanncing/loan, the bank would be able to foreclose and you'd lose the home. If you don't accept it, it will either go to a back-up beneficiary or the bank will get it.If you're not on the mortgage, then even if you're living there, you are are not forced to pay the loan living in a home does not make you responsible for a mortgage. Of course, when the home is foreclosed, you'd have to leave, but at least you would not be liable for the amount owed on it.