The Department of Health and Human Services may make payments as needed on behalf of a child who has been a ward of the department after the appointment of a guardian for the child. Such payments to the guardian may include maintenance costs, medical and surgical expenses, and other costs incidental to the care of the child. All such payments shall terminate on or before the child’s nineteenth birthday unless the child is eligible for extended guardianship assistance and medical care from the department pursuant to section 43-4511. The child under guardianship shall be a child for whom the guardianship would not be possible without the financial aid provided under this section.

The Department of Health and Human Services shall adopt and promulgate rules and regulations for the administration of this section.