Texas "at will" state for employment law...In an "at will" employer/employee relationship, either side can end the relationship (the employer can fire the employee or the employee can quit) "at will".
As an "at will" employee your options are limited. Your employer can fire you for a good reason, or no reason at all. The only thing that they can not do is fire for a "bad" reason. A "bad" reason would be if they fired you based on race, ethnicity, national origin, religion or gender some other protected class (like if you were a "whistleblower")
Here, if they fired you because they did not "have a role for you", you would not have grounds to sue.
And that is important in the question of severance....since there is no Texas law requiring severance. Typically an employer will offer severance if they want to ensure that there is no lawsuit (since to accept a severance package, you have to sign an agreement you will not sue them)
You can certainly request a severance package. But there is no law requiring they provide one
This is the part of my job I don't like...when the law is not in favor of my customer. I wish I could tell you that you are entitled to severance but I can only provide you information based on the law so that you can act on the best available information to you...I wish I had better news, but can only hope you recognize and understand my predicament and don't shoot the messenger. I'm sorry!
Please let me know if you have more questions. I am happy to help if I can. Otherwise, please rate the answer so I may get credit for my work.