Debts must be paid first, but it might be possible to mortgage the house to pay the debts and then convey the house subject to the mortgage. You need to consult with a probate lawyer.
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I am not licensed in North Carolina, but it is a pretty much uniform feature of probate in every state that the creditors have to properly file their claims in a timely manner. If they don't, their claims can be denied. They are not "just" debts. Other than a mortgage, which has a lien against the house, and Medicaid this important aspect of probate may be useful in reducing the total amount of your father's debt. You need to talk to a probate attorney.