There would still be a lien on the house that would have to be cleared. The bank would still have the right to foreclose in order to get their money back, but that wouldn't impact your credit since you aren't on the mortgage. You can be tenants in common with rights of survivorship or you can set up a trust where you are a trustee. I agree with Dave that you need to chat with a real estate attorney to determine what is the best course of action for your situation.
It is good on one hand because then the house wouldnt revert back to the state - it would go to you. On the other hand, if there is a mortgage, you would then be responsible to pay it off. You may decide at that point it is better to sell it and pay off the loan then to make the payments = but that is a decision you would have to make at that time.