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I am sorry to hear about your loss.
Did you place your name on the mortgage? The Garn–St. Germain Depository Institutions Act allows the mortgage to be transferred by inheritance to a related owner-occupant who would inherit the property. This is done as part of a formal probate process. If this was done, then you'd be personally liable for the mortgage, yes.
Otherwise, you are simply living on the property. You are not automatically responsible for the mortgage, but the lender can and likely will foreclose on the property if it is not paid, meaning you'd lose it. In addition, if probate was not filed, the lender will then issue the eventual deed in her name, complicating you having clear title to the property. So probate is not a bad idea.
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