I was fired because i refused so sing papers accusing me of thing that were not true. i was put in a room with my area manager and store manager they told me to admit to the thing written on the paper and that i would not loose my job that i will only be demoted and cut my pay . i did not sign the paper so i got fired.
It also depends on what they were trying to get you to sign. For instance if they were saying that you must sign a write up admitting you were not discriminated against (when you were) then that would be a reason to sue. You should go see a local employment lawyer and get some advice. It could also be that they were trying to force you to sign a write up that was false because they want to justify your future termination for an illegal reason -- like age. So my answer is simply that while Texas is an at-will state if the attempt to have you admit something that was false is just an excuse to fire you for a discriminatory reason (for example disability, age, sex ect...) then you may have a case for wrongful termination.
Employment / Labor Attorney
Yes they can fire you but you can probably receive unemployment benefits. In all likelihood they would have fired you after you signed it anyway.
Employee Benefits Lawyer
Texas is an employment at will state. Typically, unless an employee has an employment contract, or is employed under a collective bargaining agreement through a union, the employer can modify or terminate the employment at any time with or without cause. If an employer, at any time, decides they no longer want to employ someone, for any non-discriminatory reason, that employee can legally be terminated. However, an employer generally cannot modify or terminate the employment for prohibited discriminatory reasons (such as racial discrimination), or in retaliation for certain protected actions (such as whistle-blowing). The situation you describe does not appear to constitute prohibited discrimination or retaliation.
Your question has been answered as a courtesy. This is not paid legal advice. Nothing in this communication is intended to create an attorney-client relationship. Unless expressly stated otherwise, nothing contained in this message should be construed as a digital or electronic signature, nor is it intended to reflect an intention to make an agreement by electronic means.