Job search when coming up for tenure

I notice that coming up for tenure/getting tenure is often an opportunity to move to another institution (even if tenure is granted). How does this work in practice? Is it common for assistant professors to formally go on the job market the year that they are up for tenure? Do they do it only informally, by asking around? Do schools just make offers to up-for-tenure APs without prompting?

I'm curious how this works, because it seems that often times these moves are worked out shortly after tenure decisions are made, so it seems like they must have been in the works before hand.

I'm most interested in highly ranked US based research universities.