Does everyone I extract join Mother Base?
Inspired by this question: How do I get S+ or better soldiers? I recall that the staff at Mother Base need to convince each potential recruit to join the ranks. I've also heard a rumor that the chances are better the higher Big Boss's heroism is.
Do some of the soldiers I extract decide not to join? What are the factors that affect this decision?
Everyone that makes it to the brig will join sooner or later.
The sole exception to this rule is that when all platforms and the waiting room are at absolute full capacity, and a candidate is less effective than all existing soldiers, then they will be let go and show as "Not Hired" in the Former Staff tab.
Each soldier has a persuasion rating that drops as time passes. You can see their current persuasion progress under the Brig tab of Staff Management in the iDroid.
Also note that the "Brig" and the "FOB Brig" are two separate locations. The soldiers in the FOB brig are susceptible to abduction/rescue by FOB invaders, whereas the regular brig on Mother Base cannot be raided by other players.