Whenever the owner of such property for which a trustee has been appointed under the provisions of this chapter shall have been absent and unheard of for a period of seven years and no presumptive heirs at law have appeared and applied for the provisional distribution of such property and no will of the absentee has been presented and proven, the trustee appointed under the provisions of the chapter shall apply to the court for a final settlement of his or her account and upon the settlement of such final account the property of the absentee shall be escheated in the manner provided by law for escheating property of persons who die intestate leaving no heirs.