Except as provided in section 52.361, the personal delinquent lists allowed to any collector shall be delivered to the collector and when the collector’s term of office expires then to the successor, who shall be charged with the full amount thereof, and shall account therefor as for other moneys collected by the collector. When the collector makes the next annual settlement the collector shall return the lists to the clerk of the county commission, and in the city of St. Louis the lists and the uncollected tax bills to the comptroller of the city, and shall be entitled to credit for the amount the collector has been unable to collect. The lists and bills shall be delivered to the collector’s successor, and so on until the whole are collected.