(1)    Any county or combination of counties may establish and staff a county residential care institution for the reception and care of dependent persons which shall be governed by the county board. The institution shall be licensed under s. 50.03 by the department before receiving or caring for any dependent person.

   (2)   Residential care institutions may be established and staffed by private vendors for the reception and care of dependent persons. The institution shall be licensed under s. 50.03 by the department before receiving or caring for any dependent persons.

   (3)   Any county operated or private residential care facility not certifiable as a Title XIX facility shall be licensed and governed under s. 50.03 by the department before receiving or caring for any dependent persons.

   (4)   The cost of care of such patients shall be determined by multiplying the per day patient rate for such facility as determined by applying the formula under s. 49.45 (6m) (ag), except that interest on capital expenditures which are reimbursable under s. 51.91 shall be excluded, times the number of days of care of such patients in the time period being considered. Any amounts received by the facility from the patient or resident shall be deducted from the costs determined under this subsection. This section shall not be construed to require that as a condition of reimbursement any facility must meet any skilled or intermediate care standards established by the department.

   (6)   The care, services and supplies provided under this section shall be a liability against the patient’s county of residence.