The Department of Healthcare and Family Services may provide by rule for compromise of debt owed to the State in the form of child support arrearages and interest accrued on child support arrearages assigned to the State under Section 10-1. The rule shall establish the circumstances under which such obligations may be compromised, with due regard for the payment ability of low-income obligors and the importance of encouraging payment of current child support obligations. The rule shall provide that assigned obligations shall be compromised only in exchange for regular payment of support owed to the family and shall require that obligors considered for debt compromise demonstrate inability to pay during the time the assigned obligation accumulated. The rule shall provide for nullification of any compromise agreement and the prohibition of any future compromise agreement if the obligor fails to adhere to the compromise agreement. In addition, the rule shall establish debt compromise criteria calculated to maximize positive effects on families and the level of federal incentive payments payable to the State under Title IV, Part D of the Social Security Act and regulations promulgated thereunder.