(a) Unless foreclosure has been completed by the decedent and the redemption period has expired prior to his or her death, real property mortgages, the interest in the mortgaged premises conveyed thereby, and the debt secured thereby which come into the hands of the personal representative, or any real property acquired by the personal representative in settlement of a debt or liability, shall be deemed personalty in his or her hands and be distributed and accounted for as such. However, if the property is sold by the personal representative, it shall be sold as real property.
(b) Except as provided in subsection (a) of this section, in all cases of a sale of real property by a personal representative upon order of the court, the surplus of the proceeds of the sale remaining at the time of final settlement of the account shall be considered as real property and disposed of among the persons and in the same proportions as the real property would have been if it had not been sold.