Texas law may differ, but ion most US states. the laws of contract require that certain types or classes of contract be contained in a writing to be legally enforceable (examples: contract for sale of real estate; agreement to reaffirm a extinguished debt; a contract that requires performance for a year or longer).
Yet, even in states and circumstances where a written contract might otherwise be required for legal enforcement, where there has been part performance, the courts may also enforce the agreement in order to give both (or all) of the parties the benefit of their bargain. In other circumstances, under the laws of some states a quasi-contract may be recognized in order to avoid an inequitable result (some times referred to as promissory estoppel or equitable estoppel).
In these instances, even if all of the requirements for a contract (verbal or written) are not present, the courts may enforce an agreement to protect the reasonable expectations of one party (particularly where they have begun performance or engaged in some part performance or forbearance in reliance on an understanding that an agreement is formed.
The learning point, verbal contracts can be enforced in many states, particularly if there has been part performance, and the terms of the contract can be proven with some accuracy (sometimes by proof of the part performance).
If you have concerns about your liability for breach, or are seeking to enforce a verbal contract or agreement in Texas, your best bet is to seek counsel from a skilled business and contract attorney in Texas.
State Required Legal Ethics Disclosure: This Answer and any information contained in this answer is not intended to be treated as legal advice, but is offered solely for educational and information purposes. This posting does not create an attorney-client relationship or privilege of any kind. This attorney licensed only in Georgia.