Many years ago, a woman that worked at the same place, just didn't turn up one day. I think they (the closest thing we had to HR at the time) let this slide for a week, then called her. She just said "Oh, I didn't work to work there any more".
I don't think they pursued it any further and let it at that.
I just don't understand that mentality. You burn a bridge, when you could just send an email or something saying you quit and keep the possibility of coming back sometime open. Or if your boss actually liked you, you could have gotten a recommendation, but instead decided to make their life suck.
Just send an email saying you quit, it's really not that hard.
I thought it was weird at the time. The contracts had a notice period in, and it's not like many US states where employment is at-will. The employer is definitely required to give notice (albeit they can send you home and just pay you the notice period, which many do). So I suspect they could have gone after her for that, if they wanted to.
Likely they considered it not worth pursuing, though.
But if you're going to violate a contract anyway, might as well make dealing with that easier for your direct manager. Maybe you're unwilling to work those three months, but sending an email saying you resign at least helps your boss out. My boss put one of my coworkers on disability leave, for example, instead of firing them (he fired them when they came back after a couple months and the issue wasn't resolved).
But it all starts with actually making the most base level of effort. An email takes like 10 seconds and doesn't need to be long:
Sorry for the short notice, but I can't work here anymore and won't be coming in anymore. Know I'm supposed to give more notice, but I just can't. Sorry again.
As someone that manages people, I'd be annoyed with that, but less annoyed than if someone just stopped showing up. In fact, if they were a decent worker, I might respond with something like this:
Thanks for letting me know. Here's the documentation for short-term disability, if that's what you need. Let me know if you'd like to try that. I've started processing your resignation with the shortest possible term (X days), but I can cancel that if you let my know by <day>. I've told the team you're out sick, so coming back won't be an issue if you choose to.
I hope everything is well, please feel free to reach out, even if you just want to talk.
And if I really didn't like the employee:
Sorry to hear that, thanks for letting me know, I've started processing your resignation. Our policy is 3 months notice, and the consequence for doing that is <X>. I've attached a copy of the company policy for you to review.
You do you, but a little professionalism goes a long way. Maybe that manager moves to another org that you want to apply at, and they reject you because of how you acted the last time. Or maybe they just tell someone at the new org how you left.
Doing this has zero benefits to you, sending an email takes almost zero effort and might have some benefit for you. The rational thing is to send the email.