Legal Question in Civil Litigation in Texas

First, it makes no sense that she's suing when, as you indicate, the appliances are all paid for. Once they're paid for, her exposure to liability comes to an end. That being the case, she has no grounds to sue you. There must be some things you haven't included in your request for help. Could be tricky on the question of whether she can sue just you - assuming she has a valid basis for suing. If your name is not on the agreement, then you can argue that you are not a named party in the contract. On the other hand, there's an assumption that both husband and wife are responsible for debt incurred during their marriage. You would have to share a lot more information in order to be adequately advised.