You did not receive any services from the hospital - your mother did. She is responsible for the medical bill. Assuming you did not sign any paperwork guaranteeing payment, I see not basis for the hospital collecting from you. If your mother is uninsured, she should contact the financial services department of the hospital and see if they have special programs for uninsured patients. I believe most will work with your mother to either forgive the balance or agree to a payment plan. I would contact the hospital and point out that they are sending it to the wrong address. Good luck!