If you are joint tenants and own the house then it is both of you that own all the house as far as I know. She would be liable for mortgage payments and arrears and entitled to any profit, or a share in it. You would have to go to a solicitor to get it into your sole name and you would not be able to do that without her consent. Normally one would think of buying out the other party but in this case as there is negative equity and you can't get a mortgage on your own, then it is a problem. I suggest you speak to your lender, or perhaps the CAB