Job search when coming up for tenure
This is a manifestation of game-playing, and is completely understandable once one starts thinking in such terms.

For example, if a person is in an excellent situation to get tenure at their current institution, they are probably in an equally good position to get other jobs, perhaps with tenure.

Another feature: if a person has done good-enough work that they've got outside offers, this can set in motion the getting-tenure process at their current institution.

(Shallowly enough, the "best" certification of one's academic virtue is outside offers.)

At the same time, I think most up-for-tenure assistant profs in the U.S. are not really looking for outside offers as they come up for tenure, so even if they could generate them, they'd not try. For that matter, despite the "rewards", many people find this game-playing obnoxious so don't do it.

To answer another part of your question: yes, most formal job offers only arise after informal inquiries and back-and-forth, because... as with high-school dating... getting turned down is embarrassing. :)

The people who are interested in gaming the system continue to do so after tenure, typically...