Under Virginia law, finders are not necessaraly keepers in the Commonwealth of Virginia as the law clearly states:

§ 3.1-796.96:7. Notification by individuals finding companion animals; penalty.

A. Any individual who finds a companion animal and
(i) provides care or safekeeping, or
(ii) retains a companion animal in such a manner as to control its activities shall, within 48 hours:
1. Make a reasonable attempt to notify the owner of the companion animal, if the owner can be ascertained from any tag, license, collar, tattoo, or other form of identification or markings, or if the owner of the animal is otherwise known to the individual; and
2. Notify the pound that serves the locality where the companion animal was found and provide to the pound contact information including at least a name and a contact telephone number, a description of the animal including information from any tag, license, collar, tattoo, or other identification or markings, and the location where the companion animal was found.
B. If an individual finds a companion animal and
(i) provides care or safekeeping, or
(ii) retains a companion animal in such a manner as to control its activities, the individual shall comply with the provisions of
§ 3.1-796.68.
C. Any individual who violates this section may be subject to a civil penalty not to exceed $50 per companion animal.

Keeping the animal

Some local animal control agencies will allow you to keep the animal after reporting it as found, others may not-please consult with your local authorities for more information.
If the animal remains in your custody, you are required by law to comply with the provisions of of the Code of Virginia

§ 3.1-796.68. Care of animals by owner; penalty.
A. Each owner shall provide for each of his companion animals:
1. Adequate feed;
2. Adequate water;
3. Adequate shelter that is properly cleaned;
4. Adequate space in the primary enclosure for the particular type of animal depending upon its age, size, species, and weight;
5. Adequate exercise;
6. Adequate care, treatment, and transportation; and
7. Veterinary care when needed or to prevent suffering or disease transmission.

The provisions of this section shall also apply to every pound, animal shelter, or other releasing agency, and every foster care provider, dealer, pet shop, exhibitor, kennel, groomer, and boarding establishment.

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