Tex. Civil Practice and Remedies Code § 17.001: SUIT ON CONTRACT WITH SEVERAL OBLIGORS OR PARTIES CONDITIONALLY LIABLE.

(a) Except as provided by this section, the acceptor of a bill of exchange or a principal obligor on a contract may be sued alone or jointly with another liable party, but a judgment may not be rendered against a party not primarily liable unless judgment is also rendered against the principal obligor.

(b) The assignor, endorser, guarantor, or surety on a contract or the drawer of an accepted bill may be sued without suing the maker, acceptor, or other principal obligor, or a suit against the principal obligor may be discontinued, if the principal obligor:

(1) is a nonresident or resides in a place where he cannot be reached by the ordinary process of law;

(2) resides in a place that is unknown and cannot be ascertained by the use of reasonable diligence;

(3) is dead; or

(4) is actually or notoriously insolvent.

Acts 1985, 69th Leg., ch. 959, Sec. 1, eff. Sept. 1, 1985.