Va. Code § 55.1-2834
If any domesticated livestock, as to which the boundaries of the lots or tracts of land in any county, magisterial district, or selected portion of such county constitute a lawful fence, are found going at large within such county, district, or portion of such county, or upon the lands of any person other than the owner, the owner or manager of such animals shall be liable for all damage or injury done by such animals to the owner of the crops or lands upon which they trespass, whether the animals wander from the premises of their owner in the county in which the trespass was committed or from another county, provided that when the boundaries of lots or tracts of land in only one of two adjoining counties constitutes a lawful fence, and any of such animals escapes across the line or boundary of the two counties, the owner of such animal shall not be liable to the fine imposed by subsection B of § 55.1-2810, nor for any trespass committed by such animal upon the lands lying next to such line or boundary, nor to a forfeiture of the animal, unless the land upon which the trespass is alleged to have been committed is enclosed, as provided in § 55.1-2804.
Va. Code § 55.1-2834