If the credit card company sues a person that's dead is the family responsible for the debt?

If the account was not joint, and the person was either not married or was married and did not live in a community property state, the debt becomes part of the estate and is subject to state probate procedures. Joint account debt becomes the responsibility of the surviving account holder. Debt incurred by a married couple that lived in a community property state, regardless of a joint or single account, becomes the responsibility of the surviving spouse.