(1) After the expiration of one year from the time of giving notice under RCW 30B.44B.140(3), the director shall issue and serve by mail a final notice stating that one year has elapsed since the sending of the notice referred to in RCW 30B.44B.140(3), and that the director will sell all the property or articles of value set out in the notice, at a specified time and place, not less than thirty days after the time of the final notice. Unless the person shall, on or before such time and to the satisfaction of the director, claim the property, identify himself or herself, offer evidence of his or her right to such property, and remit payment to the director of all storage costs and reasonable costs associated with delivery to such person, the director may sell all the property or articles of value listed in the notice, at public auction, at the time and place stated in the final notice: PROVIDED, That a notice of the time and place of such sale has been published once within ten days prior to the sale in a newspaper of general circulation in the county where the headquarters of the state trust company was located.

(2) In addition to subsection (1) of this section, any such property held by the director, the owner of which is not known, may be sold at public auction after it has been held by the director for one year: PROVIDED, That a notice of the time and place of sale has been published once within ten days prior to the sale in a newspaper of general circulation in the county where the headquarters of the state trust company was located.