It is possible that Medicaid can put a lien on your ex-wife's former home that she signed over to you if you paid nothing of value for the title transfer and if the money that she owes Medicaid occurred before title to the property was transferred over to you.The reason for this opinion is that there are laws in all states prohibiting the transfer transfer of real property to defraud creditors. Possibly the transfer of the title to you may be a violation of your state's statute on the subject.