(a) Except as provided by Subsection (b), the contract establishing the rights, duties, and liabilities of an initial carrier and the shipper applies to each subsequent connecting carrier.
(b) The contract between the initial carrier and the shipper does not apply to a connecting carrier that executes a new contract with the shipper supported by valuable consideration.
(c) For purposes of Subsection (b), valuable consideration does not include the transportation of a caretaker with the freight.