The mortgage is not your personal debt, so the foreclosure should not affect your personal credit.However, as executors, you and your sister have a duty to your mother's heirs to protect the assets in her estate. You do not have to use your personal assets to save the home, but you should consider using your mother's other assets to prevent foreclosure, if it's possible. If you can sell the home instead of allowing foreclosure, you should do that. At the very least, you should get the other heirs' consent to allowing the foreclosure to take place, if you feel you must allow it.