Yes, if the home remains in the mother's name, after her death the state will have the right to recover whatever it has paid for her care under the Medicaid program. Fortunately, under the Medicaid rules, the son qualifies for an exception to the usual restrictions on transferring assets. The so-called "caretaker child" exception permits the transfer of the home to a child who has lived in the home for at least two years before the parent moved to a nursing home, and who during that time provided her with care that kept her out of the nursing home. The second issue in your case is whether the mother is competent to sign a deed transferring the home to her son. If she is not, the home may be transferred under a durable power of attorney, if one exists. Otherwise, it may be necessary to seek guardianship and court approval of the transfer. To implement the transfer and to make sure there are no local rules standing in the way, you will need to consult with an elder law attorney in your state.