Howdy!
That's a great question that LilyWan asks, and unfortunately a thread hiccup prevents direct response.
It really stumped me, as the rulebooks are somewhat unclear in this grey area, and without a forum search (luckily there was google advanced search) it was hard to scan the rules board for answers to similar situations.

"[when] Does a defeated character's turn end?"

So,
I think as _NickName_, Darth O and Sithborg have said in the past (maybe also swinefeld on some similar questions),
when a character is defeated, they're removed from play immediately, so 'the character's turn would immediately end" as a rulebook norm.

A round is the 0-2 figures activate per round - a turn is when all figures on your squad have activated.
being unactivated is required to be able to use a movement and turn, or abilities which replace turn or activation.

At time of defeat, abilities such as Avoid Defeat would trigger, as would Rolling Cleave, Riposte, etc... or conditional reserves, that kind of thing.

If they were to succeed in Avoid Defeat - they would still count as activated (you couldn't activate the figure twice in the same turn). Similar for things such as 'Pawn of the Darkside".

I hope this was feedback in a right direction (with okay interpretation),
and I look forward to hearing other rules aficionados chime in.

Also,
Lilywan, what was the game situation that needed a clarification of these rule? - was a character defeated before getting the last Gambit point, for instance?