If a spouse passes away leaving debt only in their name, their spouse is not at all obligated to pay the debt. However, if the debt is on a credit card with both names or a joint account the spouse is still obligated to pay the debt. The spouse may not get off without any consequences though. Creditors are within their rights to go after the estate of the deceased. If a mortgage is in the name of both spouses creditors may even go after half of the home. If a spouse passes away with debt the best thing to do is contact an estate lawyer. So, family members can't be held liable for a relative's debt unless the debt is in a joint account or property, like a mortgage.