The estates of all mentally or physically deficient persons who have been admitted to the state residential schools listed in *RCW
72.33.030 either by application of their parents or guardian or by commitment of court, or who may hereafter be admitted or committed to such institutions, shall be liable for their per capita costs of care, support and treatment: PROVIDED, That the estate funds may not be reduced as a result of such liability below an amount as set forth in *RCW
72.33.180.