An application under this chapter is deemed to create and effect an assignment of all rights to support, which a family member or foster child may have or come to have, to the state agency. The assignment:
1. Is effective as to all current support obligations and periods of eligibility;
2. Is effective as to all accrued support obligations with respect to a foster care child;
3. Is limited to the total cost of benefits provided to the family or foster child;
4. Terminates when eligibility ceases, except with respect to any support obligation unpaid at that time; and 5. Is not effective as to any child subject to a benefit cap imposed under section 50-09-29.