In the event any county legislative body fails to make such an annual contract, or in case all the beds contracted for shall at any time be filled, and is made satisfactorily to appear to the county mayor that a sick or injured person is unable on account of poverty to procure necessary care and medical attention, the county mayor may contract with such hospital to take charge of and render to such person the care and medical attention necessary during the illness.
T.C.A. § 71-5-2310