Could be wrong but i think they have to pay it if they want to inherit your stuff.Your family doesn't have to pay credit card bills. Once you die, all your family has to do is tell them your deceased. Only way they would be if their name is on the card.
So for example, say you own a house worth 300k but you owe a total of 200k. If you die, your kids can't just inherit the house and not pay the 200k.
EDIT: Just read your reply about it not applying to credit cards. Honestly i could be wrong but i always thought it was like that for all debt.