Texas is an employment at-will state. This means that absent a statute or an express agreement (i.e. an employment contract) providing otherwise, the employer or employee may terminate or modify the employment relationship for any reason or no reason at all.
No, no, you see, it's actually so empowering for the worker because they can quit at any time with no notice! Isn't that so empowering! In fact, I almost think that the balance of power goes too far in the workers favor on this and we need to give some of it back to the poor employers who are just always walking on eggshells since they can be quit on at any time!
/s just in case
It's so insane that anyone can argue that at-will employment is anything other than a shitty employer's wet dream.
I can leave my job with 0 notice, yet they can't fire me instantly without a good cause...and we have pretty poor workers' rights overall where I am, at least compared to the rest of the developed world.
Of all developed countries the US have by far the worst worker protections. Which has of course nothing at all to do with democracy having been usurped by the oligarchy.