@PATAX  A lot depends on the circumstance. I.e. If there was a will, most direct that debts be paid before assets distributed. Each situation stands on its own merit. 

if a decedent passes without assets, the personal debt would not be the obligation of the heirs.

@PaulaB 
The debt has been written off by the creditor. If there was an estate with assets that have been distributed, the IRS could have recourse against the estate. If a 1041 was filed, The decedents SSN is tied to the estate TIN.