Va. Code § 15.2-1651
If the land is not donated, and the fund offered is not sufficient to acquire the land and erect the necessary buildings, or if the land is donated and the fund offered is not sufficient for the purposes aforesaid, the board of supervisors may issue the bonds of the county to an amount which with the fund offered shall be equal to the amount set out in the petition, and the proceeds of the bonds with the amount donated shall constitute the fund out of which the land shall be acquired, if not donated, and the buildings erected and improvements made. If the financial condition of the county is such as to render the issue of bonds unnecessary, the supervisors may decline to issue them. However, the amount expended shall not exceed the amount named in the petition and authorized by the voters.
Va. Code § 15.2-1651