N.Y. Surr. Ct. Proc. Act § 1912

§ 1912. Effect of death of fiduciary\n 1. In the event of the death, removal or disqualification of all of\nthe fiduciaries before the granting of an order directing disposition of\nthe real property their successor must be substituted and the proceeding\nshall continue by or against the successor.\n 2. In the event of such death, removal or disqualification after the\ngranting of the order but before the complete execution thereof the\nsuccessor must proceed without further order to complete all unfinished\nmatters as were required of his predecessors.\n 3. The successor must give such security for the performance of his\nduties as the court may require.\n 4. If no successor is appointed the court may make an order\nauthorizing the fiduciary of the last surviving fiduciary, on giving\nsuch security as the court may require, to continue the proceeding or to\ncomplete all unfinished matters as were required of the fiduciary.\n