The standard for getting unemployment benefits is different from the standard for bringing an employment law claim under Federal or State law. The Texas Workforce Commission considers whether the fired employee was terminated because of “misconduct.” "Misconduct" under the law of unemployment compensation is basically something that the claimant did or failed to do that 1) caused a problem for the company, 2)was in violation of a rule, a policy, or a law, and 3) was within the claimant's power to control or avoid.
A termination that is unfair or based on accusations that are not accurate generally does not in and of itself create a claim for unlawful discrimination or retaliation. It’s important to talk to an experienced employment lawyer to learn about your rights.