You do not give any information about what has prompted the question. Are you considering moving away and just leaving it with them? Are you concerned about what happens after your death? The answer to your question may be influenced by the particular facts.
If you die, the ownership of the property may well go to your boys under your will (or by State law if you leave no will). In that event, the lender would surely not be concerned with anything other than receiving its money. How the title becomes vested as a result of your death would just have to be agreed upon by the boys. If they don't make the payments, they would lose the property to foreclosure.
If you are thinking of just moving away and leaving it with them, things will work out probably differently. It is doubtful (though not necessarily so) that the boys will like the idea of making payments on property they don't own. And the bank will certainly foreclose if they don't make the payments.
Answered on Jan 13th, 2012 at 2:47 PM