They can court martial you, hit you with insubordination beforehand, delay the paperwork, all kinds of fun stuff, because despite being a volunteer army, you sign an enlistment contract and unlike at-will employment that gets pushed everywhere else to combat unions, there can even be financial consequences for trying to leave your contract early.

It's why I heavily discourage people from joining the military, other than all the usual reasons. At least you can quit McDonalds.

So there are different levels of discharge and some of the worse levels, “Other Than Honorable” and “Dishonorable”, will supposedly make it difficult to get hired (assuming employers know about it) and result in (I think) total loss of benefits on top of that. In addition, their superiors could find creative ways to make their life very difficult and they’ll likely face harassment, extreme punishment, and possibly physical/mental abuse. If they’re convicted of something, they could also be locked up in a military prison.

Someone on their side with good knowledge of the military legal system can potentially help protect them from all this which would of course help them to make a decision to refuse orders and/or leave completely.

I think I’ve mentioned it before, but convincing soldiers to find a way out and helping them do so seems like good praxis for multiple reasons and I wish there was more discussion about this.