When a person dies do their bills die with them?

costs more to leave than arrive

No, the person may die but, their bills go on until paid by either surviving family or liquefying the remains of their estate.

The bills go to the estate. Any debts owed are to be paid from the proceeds of liquidating the estate. This can include life insurance if it was a part of the estate, but if the life insurance goes to a specific beneficiary, that money is not considered part of the estate.

If the deceased owned property and there is no cash in the bank to satisfy the debts, the creditors may require that the property be sold to satisfy the estate. In short, no, the debts do not die with them until all of the estate has been satisfied. That's why probate courts end up costing so much.

(Family members are not required to assume responsibility for the decedent's debt.)