Surplus proceeds arising from the sale or mortgage of the real estate of a deceased person by an executor or administrator, or from the sale or mortgage of the real estate of a ward by his or her guardian, remaining on the settlement of the final account of the executor, administrator or guardian, shall be considered as real estate, and shall pass to, or be distributed in the same proportions among, the same persons who would have taken the real estate if it had not been sold or mortgaged.
R.I. Gen. Laws § 33-19-23