If the surviving spouse was listed as a co-borrower or a primary account holder, they will be obligated to repay all debts associated with the credit account. If the surviving spouse was listed as a supplemental cardholder on their late partner’s credit card account, they will not have to personally pay off the debt. However, if a person owes money when they die, the value of their estate is used to pay back creditors. As a result, the bill may have to be paid via shared assets (or assets that you expected to inherit).