(a) If a bank selected to be a county depository and holding county funds is sold to another bank in an adjoining county, the successor bank in the adjoining county may continue to serve as a county depository and apply and be selected as a county depository if the successor bank:
(1) continues to have an office in an adjoining county; and
(2) timely applies and is selected to be a county depository in a manner that ensures no lapse of service as a county depository.
(b) If a bank selected as a county depository and holding county funds closes, a branch of the bank in an adjoining county may continue to serve as a county depository and apply to be a county depository if the successor bank:
(1) continues to have an office in an adjoining county; and
(2) timely applies and is selected to be a county depository in a manner that ensures no lapse of service as a county depository.