The Secret Service would carry him out. The American bourgeoisie and nat-sec state have no loyalty to Trump and see Biden as a more stable imperialist tool they can use. Besides they need to preserve the illusion of democracy which is more important than any one tool of theirs. If the Republicans cannot rig it in such a way that Trump wins clearly (ballots not being counted or incinerated aside) and they can’t finagle up some sort of excuse for the Supreme Court to step in to help them they’re done and he’s out. Simple as that.

He’s not president after Biden gets inaugurated and there is really nothing to indicate that the military is going to do a coup for him.

He’d stick around for a few days right up until the point where the Senate is threatening to send the capitol police to pull him out, ensuring it would be a massive spectacle. He’d surrender, but claim to have been ousted by the liberal elitist deep state under unfair, fake election results. He then claims to be the true winner then goes on to have a successful media career where he constantly brings up how he’s the real president.

It sounds like a pretty good deal overall for him.

Legal battles and spectacle. The media will love it. People will probably riot in the same ways they have been this year. The cops and national guard will be deployed everywhere needed to bring “stability.” It’s all disorganized so it won’t foment into anything proper, but a lot of fence-sitting libs and electoralists will be pushed left at the obviousness of corruption. After that, nothing much else will change though, doesn’t matter which candidate.

If I’ve learned anything from the past four years, it’s that our government basically works on the Honor System.

So to answer your question, I guess nothing.