Va. Code Ann. § 21-308

After the time of publication shall have expired, if no person claiming and asserting title to the tract or tracts of land and entitled to notice shall appear, the court or the judge thereof, in its or his discretion, may appoint some disinterested person to represent the unknown owner or owners of the lands, and thereupon the court shall assume jurisdiction of the tract or tracts of land, and shall adjudicate as to the lands to the same extent as if the owners were present and represented, and shall proceed against the land itself.