If a credit card holder dies and authorized user is not responsible for the bill can the authorized user's credit be damaged for not paying the bill for which they are not responsible?

It depends on the fine print. If the credit card company determines that you received benefit from the use of the card, you can be held responsible for the charges. If the estate of the deceased has resources the card should have been paid off and terminated upon the death of the holder. Any use use of the card after the death of the cardholder most likely constitutes fraud, especially if the subsequent user did not pay for the card balance. But you'll need to read the terms of the use agreement to verify that.