When a guardian, trustee, or other person holding an estate or interest determinable upon the life of another person, shows by affidavit or otherwise to the satisfaction of the court, that:
he may continue in the possession of the estate, and receive the rents and profits for and during the infancy of the infant, or for and during the life of any other person on whose life the estate or interest depends.
D.C. Code § 16-1157