Upon the death of any county collector during the time the tax books are in his or her hands, and before the time for making settlements, the county clerk shall take charge of the tax books. The clerk shall appoint one or more competent persons to examine the tax books. The appointed persons shall ascertain the amount remaining uncollected, and make out an abstract of the same, except that if there is only a small portion of the taxes collected at the time of the death of the collector, the amount actually collected shall be ascertained, and the same books used in completing the collections.