If an executor or administrator die, resign, be removed, or become incompetent, letters of administration de bonis non with the will annexed, or de bonis non, shall be granted to the person entitled, and he shall proceed in the administration of the estate. The letters, bond, and oath shall be in the common form, substituting proper words to show the character of the administration. The executor of an executor shall not be entitled, in right of his office, to administration de bonis non of the first estate; but such executor, or the administrator of an executor, or the executor or administrator of an administrator shall settle the accounts of his testator or intestate in the administration of the first estate, and for that purpose shall be amenable to the jurisdiction of the court.