The Department shall enter into intergovernmental agreements to conduct monthly exchanges of information with the Illinois Department of Corrections, the Cook County Department of Corrections, and the office of the sheriff of every other county to determine whether any individual included in an assistance unit receiving public aid under any Article of this Code is an inmate in a facility operated by the Illinois Department of Corrections, the Cook County Department of Corrections, or a county sheriff. The Illinois Department of Corrections, the Cook County Department of Corrections, and the office of the sheriff of every other county shall honor all intergovernmental agreements with the Department under this Section and shall provide all required information in a timely manner. The Department shall review each month the entire list of individuals generated by the monthly exchange and shall verify the eligibility for benefits under this Code for each individual on the list. The Department shall terminate benefits under this Code for any individual determined to be ineligible by this monthly review. The Department shall use any legal means available to recoup as an overpayment any assistance provided to an individual for any period during which he or she was ineligible to receive the assistance.