Any duly appointed conservator of the estate of a person who is known to be dead or who is presumed to be dead pursuant to Chapter 23 (§ 64.2-2300 et seq.), after making a diligent but unsuccessful effort to locate the heirs of such person for a period of at least two years after the person’s death became known or presumed, may petition the court having jurisdiction over real property owned by the decedent for permission to sell such property. Proceedings under this section shall conform as nearly as practicable to proceedings relating to judicial sales of real property owned by an infant. The conservator shall account for the proceeds of the sale, and the net proceeds of the sale, after disbursement of costs, shall be conserved in such manner as the court deems proper.