I would not let the house go to auction. That will be the least advantageous. Having her sell now means that she has to have the balance of the mortgage available at closing to pay down the loan. That would of course reduce the value of her estate and then it’s less going to the grandkids or whoever. Whether she or her estate sells when she is alive or afterward is likely moot. She still owes the bank the balance of the mortgage no matter what.