If you were my employee and I said you had a shift at say 8am and you never showed up then I'd just fire you _with cause_. There's no need for it to count as a resignation.
Looking at Texas's site [1], they explicitly say if your employer asks for a resignation it counts as being fired. There are also a bunch of ways for quitting to be eligible (i.e. "Significant changes in hiring agreement").
[1]: https://www.twc.texas.gov/jobseekers/eligibility-benefit-amo...
The employee will often need to sign a statement of resignation (Termination by mutual agreement), but the employer can absolutely initiate and send them the paperwork.
If you refuse, the resignation paperwork goes away and is replaced with firing paperwork, which you are not required to sign.
Here is some additional info: https://swartz-legal.com/what-are-the-different-types-of-sep...