There is always the possibility that your sister's creditors could seek payment from you or your husband for payment of your sister's debts. However, from a legal perspective, neither you nor your husband are legally liable to pay debts of your sister to creditors if you never signed a written agreement to do so.That is the law in all states in this country. If your sister is working and living in your home rent free, she should start trying to pay off her creditors in an agreeable monthly amount set forth in a written document signed by her and a representative of the given creditor.