If a person has any assets then the assets will likely be sold to pay off the deceased persons debt if the assets didn't go to somebody else in a will.
If they didn't have any assets or anything that the debt collectors could take then the debt collectors will just be out of luck and have to write the debt off as a loss.
Now if the debt owed is in a spouses name when the person dies then the spouse will become responsible for the debt owed and the debt collector can go after the spouse.
But that's only if the spouses name is on the debt. If the spouses name or anyone else's name is not on the deceased persons debt then they're not responsible for paying back the debt.