Upon the resignation or termination of the district superintendent, the staff members of the district office, the chief executive officer or any subsidiary and/or affiliated corporations of the district, paid and unpaid, such as assistant superintendent and office secretary, shall submit their resignations effective concurrently with the final date of the district superintendency. However, one or more of the staff members may remain with the written approval of the general superintendent in jurisdiction and the District Advisory Board, but not longer than the date of the new superintendent’s assumption of duties. (245.3)