In the US, some types of debt aren't inherited in the normal fashion, but they have to be settled by the estate, which often is is your spouse or kids. Probate Court may make the executor liquidate the entire estate. Can be an issue if people are still living in the house owned by the deceased.
Also, debt is entirely passed on in the event of a cosigner.
Plus, while credit card companies aren't supposed to, they have been known to harass family members over debt after someone passes.