Va. Code § 15.2-3829
If a town becomes a city under this chapter, the city shall assume and provide for the reimbursement of the county of a just and reasonable proportion of any county debt existing at the date the town becomes a city, including any debt existing on any school district of which the town was a part.
The city council and the board of supervisors shall make an equitable adjustment of such debts. In making such adjustment the parties shall consider (i) the city's just proportion of money collected by the county treasurer under § 15.2-3828 and of any unexpended balance in the county treasury belonging to any fund to which the territory embraced in the city has contributed and (ii) all other equitable claims of the city, county and district. If the parties fail to make such adjustment, either party may proceed against the other by a bill in equity in the circuit court for the county in which the former town lies for a proper adjustment of such matter.
Va. Code § 15.2-3829