N.Y. Soc. Serv. Law § 152-B
If, after the full amount expended by a public welfare district for the assistance and care of a deceased or other former recipient of public assistance and care, including the federal and state shares thereof, as determined in accordance with regulations of the department, and any authorized amount expended for the burial of such deceased recipient, shall have been recovered and deducted from the net proceeds of assets which have been transferred or assigned to the public welfare official by or on behalf of such recipient to insure repayment of the cost of his assistance and care, any balance or surplus remains, it shall be credited forthwith by the public welfare district to the estate or persons entitled thereto; but if unclaimed within four years thereafter by those entitled thereto it shall be deemed abandoned property and be paid to the state comptroller pursuant to section thirteen hundred five of the abandoned property law.
N.Y. Soc. Serv. Law § 152-B