Typically, and there will be the odd loop hole or odd country or state that has some sort of clause, a spouse is not responsible for credit card debt. If the credit card is in both names then of course the surviving spouse must pay the debt off.
It’s not quite as simple as all that unfortunately. If a person dies with credit card debt, their family does not need to pay that debt off, but the estate of that person does have to pay the credit card debt. So if the deceased bequeathed their estate to the family, the family would not see that money until the debt was paid off. Technically the spouse or other surviving family members would be paying that debt off, out of their inheritance. If there is no estate to collect from the debt is never repaid by anyone. As usual it takes quite a bit to beat ‘the man’.