What happens to the person that I have as a users on a credit card if I file Chapter 7?

If you are asking whether an authorized user is liable for the primary signatore's obligations on a credit card, the answer depends on the laws of whatever state governs the contract and, most likely, whether the authorized user signed the cardholder agreement.  In most cases if they did not sign the agreement, then they are only liable for the actual charges they made on the card (where they signed for the charges).