Your questions does not make complete sense, if you pay off the bills then there would not longer be a lien on the home? As far as transferring the property to your name you really should meet with an estate Attorney before making any changes on the title of the home.
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My answer provides information about the law based on the limited information provided in the questions asked and is not intended to be legal advice. The law differs in each jurisdiction and may be interpreted or applied differently depending on the location or situation. I highly recommend that you consult with an attorney to discuss the specific details of your situation so you can get legal advice tailored to your specific circumstances. The information in my answer is for educational and information purposes only, and is not legal advice or legal opinions. The answer provided to the question asked does not constitute a lawyer-client relationship.
You would have to check with an attorney in your locale, but I would consider this a fradulent transfer and if I were the creditor for the bills you do not pay I would attempt to challenge the transfer to you. having siad that you should talk to an attorney who does estate planning. You may be able to transfer the property to you and let your parents keep a life estate that cannot be attached if your parents are sued.
If you pay off all of their creditors, then there is no problem. If you only pay off the liens and take possession of the property, the remaining creditors can come after you. Unless you pay fair market value (or close to it), it can be considered a fraudulent transfer.
Talk to an estate planner in your state to find out how to protect the house.
[This communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.]