I don't have a lot of experience with this being that im only 15 but, when you get married it's because you love that person and you want to spend the rest of your life with them, i.e. for better or for worse, 'till death due you part. If that spouse wants out of a marriage because they dont want to pay medical bills then I would say that it wasn't a very strong relationship to begin with if something like that can seperate them. And why would they want to stay permanently together seeing how one didn't want to pay the medical bills for the other which put even more hardship on that person ontop of what they were already going though. As for the wedding ring issue, that's just another sign that they weren't committed to the other person. It sounds to me that they would be better off separated anyway.
I hope this helps you in some way! Good Luck and God Bless!