(a) Except as provided by Subsection (b), the comptroller shall register refunding obligations on surrender and cancellation of the obligations to be refunded.
(b) The comptroller shall register refunding obligations without the surrender and cancellation of the obligations to be refunded if the ordinance or resolution authorizing the issuance of the refunding obligations requires that:
(1) the obligations be sold at public or private sale; and
(2) the proceeds from the sale be deposited:
(A) in a place where the underlying obligations are payable; or
(B) with the comptroller.

(c) Refunding obligations to which Subsection (b) applies may be issued in an amount sufficient to pay the principal of and interest on the obligations to be refunded to the option or maturity date of the obligations.