If a parent chargeable with the support of a child dies leaving it chargeable upon the human service zone and leaving an estate sufficient for its support, the department of health and human services, in the name of the human service zone, may claim provision for its support from the parent’s estate by civil action, and for this purpose may have the same remedies as any creditor against that estate and against the heirs, devisees, and next of kin of the parent.