D.C. Code § 42-811
In case of the death of a sole mortgagee or trustee, or the last survivor of several, if the debt secured by the mortgage or deed of trust shall not have been paid, the party entitled thereto may file a petition in the court having probate jurisdiction, setting forth under oath the execution of the mortgage or deed of trust, the death of the mortgagee or trustee, and the fact that the debt secured by the said mortgage or deed of trust remains unpaid, and such other fact as may be necessary to entitle the petitioner to the relief prayed, and praying for the appointment of a trustee to execute the trusts of the said mortgage or deed of trust. It shall not be necessary to make the heirs at law or devisees of the deceased mortgagee or trustee parties to such proceeding. The court may thereupon lay a rule upon the debtor or parties whose property is bound by said mortgage or deed of trust, unless they shall voluntarily appear and admit the allegations of the petition, to show cause, under oath, on or before the 10th day, exclusive of Sundays and legal holidays, after the service of such rule, why the prayer of said petition should not be granted. If said party or parties can not be found in said District, service of said rule shall be by publication, according to the practice in equity in said court. If no cause be shown, notwithstanding the service of said rule, against the prayer of said petition, the court may determine in a summary way whether said debt remains unpaid, and if satisfied thereof the said court may, by decree, appoint a new trustee in the place of the deceased mortgagee or trustee, and vest in him all the title at law and in equity, and all the powers that had been conveyed to and vested in the deceased mortgagee or trustee. Nothing contained in this section shall prevent the appointment of a new trustee pursuant to § 42-814(b) and the execution of the trusts of said deed of trust by such new trustee.
D.C. Code § 42-811