There are material facts you do not include in your question that have a significant impact on the resulting answer. Are the cardholder and the authorized user married to each other? What agreement did the cardholder and the authorized user have regarding the charges the authorized user made? What history did the two have regarding the balances in the past? Why was the authorized user on the account, and for how long?
Let us say for the sake of argument that the two parties are not married to each other and had a verbal agreement that the authorized user would pay for the charges he or she made on the account. Changing the facts slightly, let us assume that the two parties had a history of the authorized user repaying the charges made in a timely manner. In both of these situations, the cardholder has a reasonable expectation that the authorized user will reimburse the cardholder for the charges made. In this situation, the cardholder has a cause of action to file a complaint to recover the amount the authorized user charged.
Let us say for the sake of argument that the cardholder and the authorized user are married to each other. In that case, both spouses are responsible for the debt in most jurisdictions.
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