Well technically, being taken out in one branch does not automatically keep one from competing in the other two, as long as at it is logically plausible (being unconscious or dead isn't particularly conducive to social discourse, but being socially humiliated rarely prevents one from throwing a punch).
Since Physical conflicts tend to have the highest immediate stakes (pretty hard to be talked to death, though some of my high school teachers tried really hard), I wouldn't consider the Social conflict "ended" so much as "deferred" while the more immediately dangerous Physical conflict is resolved. Provided participants on both sides survive the fight (via concessions, or whatnot), the Social conflict could resume. Perhaps the defeated Red leader still has some intimidating "I'll get you next time, Gadget" commentary to throw out as he is being hauled off, threats of vengeance against loved ones, and such.
If you're feeling particularly ambitious, the Social conflict could even continue during the Physical conflict, with taunts and mind games and the like.
Fate rules are designed to be heavier on the narrative than the crunchy, so the best answer is probably to find whatever version works best for your group and makes for a fun scene.