In the event the task of administering a county’s pro rata share of the county aid fund is placed on the department of transportation by resolution as provided in § 54-4-103, and, in carrying on the work on the county roads and bridges, an employee or other person is injured or killed or property damage caused so as to render the department liable to an award of the board of claims, then the award shall be paid out of the county’s pro rata share of the county aid fund, regardless of whether the funds are being administered by the department on the date of the award.