We are going through this with my Father in law...
Basically when you die, your assets (the house, money, and all other property) stand good for your debts. So if he had more debt than assets, then yes the house and all other assets will likely be sold to cover the debt.
The estate will need to be probated especially if there is real estate involved. Who gets what varies state by state, sometimes the funeral and legal costs are paid first, secured creditors (the mortgage company, a car loan) will get to recover their security and all others get what is left. If you assets are worth more than your debt, you are solvent, if not you are insolvent. Of course they will want to get legal advice on this situation…
Also you do not inherit debt, so the children do not personally owe any debt unless they co signed on anything. This however doesn’t stop the creditors from trying to get you to pay…
Again they should seek legal advice from a good probate lawyer…