The bank will claim the dues from the estate that is under the deceased name. This can include but not limited to EPF, bank, estate, etc.
There is such insurance but it need to be subscribed before the cardholder is deceased and not every bank offers it.

Interesting as the last 7-10 days many people come in here (CC section) with question that can lead to build cc debts without realizing the consequences if the whole thing spirals out of control. In most cases, they have the perceived notion that they know what they are doing.

Myself being brushed off one too many times by 'kids' who are cc novice but think highly of themselves.