This came up recently at my table, when I had an NPC concede during a fight.
The question raised by my group was when can concessions be made?
The way I've been running them is that they can be made any point before the dice roll that takes them out, as it says on pg. 206 of YS. In the session this happened, an NPC was clearly losing the fight and I wanted to get him out of it before the players killed him. So when it came around to the player who was fighting him, before the player rolled, I conceded. There was some disagreement about whether or not this was fair.
Some players argue that concessions have to happen on the NPC's turn, while others say having them happen on the NPC's turn isn't fair.
Personally, I've always thought concessions were meant to happen right before an attacker rolls their dice, so it's the choice between taking a sure way out of being killed/captured, and taking the risk to see how the dice roll.
Based on a reading of the rules, it seems that, aside from the fact you can't concede after an attack roll that would take you out, you can concede whether you like.