He won't show up to the office in August, but promises to do so by January. Until then, he keeps programming as he always has. If they want to fire him, that's fine, let them fire him so that he gets the full severance package (unemployment benefits, etc. etc.)
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...
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...