You don't have to do anything to "protect" yourself from being responsible for her medical bills. You are not responsible for her medical bills. She is an adult. Regardless of who is the subscriber to the policy, you are not responsible for any medical bills she incurs unless you sign something that says you are.
Two things I am tired of typing: 1.) A wrongful termination does not mean that you were fired for something you didn't do; it means that you were fired for a reason prohibited by law. 2.) The above answer, whatever it is, assumes that no legally binding contract or CBA expressly says otherwise. If it does, the terms of the contract apply.