I am not an attorney/lawyer, so this answer will of necessity be a lay answer until it can be improved by a more qualified source.
Usually, in most states the debts of a deceased do not just "go away or disappear." The "estate" is legally responsible for his debts. Of course, IF a deceased had no money or property [real or personal], then there IS NO estate, and there really are no heirs, and they do not have to pay the debts of the deceased.
On the other hand, IF there is money or property [real and/or personal], then there is an estate, and the estate is legally responsible to pay just [legitimate] debts of the deceased. If there is no cash money in the estate, then the property of the estate must be used to pay the legal debts.
Those debts are legally the responsibility of the estate. That means that if the deceased had any money or property, the debts must be paid before any distribution of those assets to the heirs. If there is enough money in the estate, then it is used to pay off the legal debts of the deceased.
IF there is no money, or not enough, AND the heirs do not want to sell the property [real and/or personal] of the estate to pay the legal debts, and since the debt must legally paid, that means the heirs must pay the estate debts.
If your deceased father had a home equity loan are the heirs now responsible for paying it off IF THEY SELL THE HOME?
It will come from the deceased person's estate.
Unless he had insurance to cover bills in the case of his death, the creditors will be looking to the heirs of his estate to pay them. The issue will more than likely be presented by his creditors in the Probate court.
The estate will be responsible for any taxes. It must be resolved before the estate can be closed and anything distributed.
The debts are paid from the deceased's estate, before the heirs inherit what's left (if anything). Debt is not inheritable though, so if the estate isn't enough, the heirs are not responsible for the remainder.
If the debt exceeds the assets, the assets must be sold to cover the debt. Heirs are not responsible for any remaining debt. Certified letters along with a certified death certificate should be sent to each debtor that can not be paid in full after the sell of assets. In this case there would be no inheritance.
The heirs are not legally responsible for paying the loan. However, if they want to keep the property the loan must be paid or the lender will take possession of the property by foreclosure.
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It is not the parents but the estate that is responsible for any remaining debts. That will include medical bills. If there is not enough in the estate to cover them, someone will not get paid and the heirs may get nothing.
The estate is responsible to pay outstanding debt before being distributed to the heirs.
The estate is responsible for the debts of the deceased. None of the assets can be distributed until the debts have been paid. The bank has a prior lien on the property. The foreclosure of that mortgage will not affect the heirs in any way except to deprive them of inheriting the mortgaged premises. If the heirs wish to maintain that property then they would need to negotiate with the bank and pay off the mortgage. The foreclosure will not affect the credit records of the heirs.
The estate has the responsibility to settle all debts, including utility bills, not the heirs. Once that is done, the remainder can be distributed.