Legal Question in Wills and Trusts in Virginia

If the child was not adopted, and the biological parents die without a will, the child is in a position to inherit. If there are wills, the estates of each parent will be distributed in accordance with the wills; the child has no rights to the parents' estates as against their wills.

If you mean a biological parent who dies intestate(without a will), whether

a particular child had been (allegedly) abandoned by such parent would be

totally irrelevant to the child's eligibilty to inherit from such parent's estate

(in my opinion).