Whenever any notice and finding of responsibility, or appeal therefrom, shall have become final, the superior court, wherein such person or persons reside or have property either real or personal, shall, upon application of the secretary enter a judgment in the amount of the accrued monthly charges for the costs of hospitalization, and/or the costs of outpatient services, and such judgment shall have and be given the same effect as if entered pursuant to civil action instituted in said court; except, such judgment shall not be the subject of collection by the department unless and until any outstanding judgment for a victim referenced in RCW
43.20B.335 has been fully satisfied.