Va. Code § 63.2-402
If any county or city through its appropriate authorities or officers fails or refuses to provide reimbursement of the Commonwealth, the Board shall authorize and direct the Commissioner to file at the end of each month with the State Comptroller and with the local governing body of such county or city a statement showing all disbursements and expenditures, including administrative expenditures, made for and on behalf of such county or city, and the Comptroller shall from time to time as such funds become available deduct from the funds appropriated by the Commonwealth, in excess of requirements of the Constitution of Virginia, for distribution to such county or city amounts required to reimburse the Commonwealth for expenditures incurred under the provisions of this section. All funds so deducted and transferred are hereby appropriated for the purposes set forth, and shall be expended and disbursed as provided in § 63.2-403. Any county or city may provide such other necessary or incidental social or rehabilitative services as may be authorized by the Board in connection therewith.
Va. Code § 63.2-402