Any defendant in an action brought under either § 46b-215 or 46b-216 may, at any time thereafter, prefer his complaint to said court against such survivor, the Commissioner of Social Services, selectmen or other persons, plaintiffs in such action, to be relieved from such contribution. In any action brought under said § 46b-215, the defendant in a IV-D support case as defined in subsection (b) of § 46b-231 may prefer his complaint to the family support magistrate serving the judicial district where the order was entered against the plaintiff in such action to be relieved from such contribution. If said court or family support magistrate finds that he, being liable under said § 46b-215, is required to contribute an amount beyond his ability or beyond what is requisite for such support, or that he, being liable under said § 46b-216, is required to contribute beyond the amount received by him from the estate of such deceased or beyond what is requisite for such support, it may again direct how much, if anything, he shall contribute therefor. If the contribution of the person or persons liable to support such poor person, as fixed by the court, is insufficient for such support, the remainder of such support shall be furnished by the state or such town.