Notwithstanding any other provisions of law, the department shall not be required to expend public funds for the purpose of providing support, care, and treatment covered under this chapter to any patient until such patient has exhausted his or her eligibility and receipt of benefits under all other existing or future private, public, local, state, or federal programs or plans. Before the department expends public funds for a patient's cost of care, the department may assess and recover the cost of a patient's care from the patient or other persons liable for such patient's cost of care if such patient is eligible for benefits under any other program or plan. In the event the patient is covered by an insurance contract or any other plan or benefit of any nature providing for payment of hospitalization, medical expenses, and other health care services or any combination thereof, such patient or other person liable for the cost of care of such patient shall pay or cause to have paid from such insurance, plan, or benefit without deduction, exemptions, or credits, the full cost of care of the patient, or that portion thereof covered by such insurance, plan, or benefit. The assessment for cost of care of the patient made by the department pursuant to Code Section 37-9-5 shall be for the total amount payable by such insurance, plan, or benefit up to the total cost of care or for that portion of cost of care payable by such insurance, plan, or benefit; and if the proceeds from such insurance, plan, or benefit are less than the total cost of care, such assessment shall include an assessment based on the remaining balance, except where full payment of the balance or a portion thereof is required by a health insurance program or other plan or benefit, in which case the balance or at least the required portion thereof will be the assessment. Further, the department shall comply with all federally funded health and medical insurance programs which require established amounts payable by beneficiaries and is authorized to accept amounts payable toward cost of care under any insurance program, plan, or benefit if paid according to the provisions of such programs, plans, or benefits even though the amounts payable may exceed cost of care amounts as provided by this chapter. The department shall develop procedures to apply the provisions of this chapter, specifically Code Section 37-9-5, to any amounts which remain payable by the patient or beneficiaries under a federally funded health and medical insurance program, provided that the application of any such procedures does not invalidate payment of benefits under the program. For the purpose of carrying out this Code section, the department is authorized to accept assignment of benefits payable under such insurance, plans, or benefits; but the department shall not require the assignment of such benefits as a condition precedent to the admission of a patient to a hospital or as a condition precedent to providing services for such patient. In order to collect maximum benefits payable toward cost of care, the department is authorized to contract with any insurance program, plan, or benefit to become a participating member hospital if payments are not made or are made at a lesser than full coverage amount to nonparticipating members. Moreover, the department or its designated agents will have subrogation rights to the recovery of a patient's cost of care that the patient or other person liable for the patient's cost of care may have against any person, estate, organization, entity, or plan. Further, if any patient or other person liable for the cost of a patient's care receives benefits or funds in settlement, judgment, or otherwise for any health care, medical expenses, or hospitalization or other care directly related to services and care provided by the department to a patient, the patient or other person liable for cost of care will pay or cause to have paid the full cost of care or that portion thereof recovered which is directly related to the care provided by the department. This right of subrogation is cumulative and in addition to any other remedy and this right shall be available for any enforcement or collection process which is contemplated under other provisions of this chapter.