The parents of a minor child for whom care or support of any kind has been provided under the provisions of this chapter shall be liable to reimburse the state for such care or support. Upon receipt of foster care maintenance payments under Title IV-E of the Social Security Act by a minor child, the right of support, past, present and future, from a parent of such child shall, by this section, be assigned to the Commissioner of Children and Families, and the parents shall assist the commissioner in pursuing such support. On and after October 1, 2008, such assignment shall apply only to such support rights as accrue during the period of assistance, not to exceed the total amount of assistance provided to the child under Title IV-E. Referral by the commissioner shall promptly be made to the Office of Child Support Services of the Department of Social Services for pursuit of support for such minor child in accordance with the provisions of § 17b-179. Any child who reimburses the state under the provisions of subsection (l) of § 46b-129 for any care or support such child received shall have a right of action to recover such payments from such child’s parents.