Okay, so as the result of a Firefight an NPC has captured a PC. Those were the stakes. NPC has PC trussed up, a gun pointed at his head. Is it acceptable for the NPC to just execute the PC?
I would say no. If the stakes of the Firefight were “the PC gets executed,” it would be a different story.
However, “capture” can mean many different things, many of which may still allow the PC to be playable. In fact, I’m guessing that’s why the player agreed to the stakes - he wanted his PC to still be playable. Maybe the NPC tortures him for a bit, maybe the two strike a deal (a la DoW) that is obviously in favor of the NPC. There are a couple different ways to take this without removing a player from a game.
Dude! Torture him… then DoW him into doing something he would normally find despicable! His BoA would take a crazy hit if you torture him enough. 
holy crap. tough situation.
in the past I would totally wuss out and do something lame like, leave the pc severely beaten but not dead. Then I realized that turn the tables around, and PCs are always bloody slitting throats of captives any chance they get.
So now, I would execute, so long as its in character and it makes the story freakin awesome.
Also, the player could spend a persona point to get a Complication.
This could be his out.
Sanj
I think there may be a decent discussion on the value of PCs versus the value of NPCs related to the above topic. If anyone is interested, I’ll be starting a thread in the appropriate forum shortly.
I think it’s totally acceptable to kill him.
However, I’d talk with the player 1st. I’d ask, “This what you want?”
And: there are so many more interesting things to do than just kill him. I like to think about it like a TV show. Presumably, the episode just ended with him tied up and the gun to his head. Great! Now what? Just killing him in the opener would be boring. Escape? Last minute rescue? Asked to do a terrible thing?
Also: where the hell are the other players? How could they help out?
But again, key idea: does the player want his guy to die? If so, blam! If not, talk.
Why isn’t he hulling him?
Luke,
Because he’s not a Vaylen. 
He’s just another human that the PC has antagonized to the point of wanting bloody revenge.
xenomouse,
From what I understand of the rules, “the PC gets executed” CANNOT be the stakes. You cannot make a character death a part of the stakes but it can occur incidentally.
Everyone,
For the record, what we ended up doing was a Duel of Wits where the character’s life was the stakes. That was what I decided on after trying to figure out my options for killing him, which spawned this thread.
I apologize. I only noticed this was a BE question after I posted my first response.
I believe that this is the right way to do it, one conflict or building scene to capture, a second conflict to execute. Now if this was a straight-up gun fight using the ICHASHITF (or firefight) rules that would be a different story but the stakes from the outset can’t be “lose this DOW and die.”
You can execute him, but you need to do it in a Building scene and technically make a versus Close Combat test. Obviously, your target would have severe obstacle penalties. However, the scene structure really shines here. Cut away and create dramatic tension. Let the other players have their scenes. Even tied up with a gun to his head, the other player gets to have his conflict/builder/color/interstitial. It’s very cool when this happens, because everyone knows what’s on the line, but there’s a lot of drama in playing out these last few dramatic moments! Also, rescue attempts are totally within the power of the other players. I could feasibly pull one off in a single builder.
Good times!
-L
Yeah, I had my players try to Circle into my Building scene to gain an ally to save a key NPC from getting hulled, we had time to allow them a quick second Conflict in the maneuver. They failed, and actually strengthened my position. But it was cool that they tried to do this though this was happening a few days by FTL out into space and all the PCs themselves were on the planet.
One thing I noticed in Bret’s case, and would like to ask a question about; If a player tried to Circle up someone “loyal” and already at the scene in a position to try a rescue (say they were on the winning side but had a problem with killing someone that was in a helpless positon) that would that be a +3 Ob for scene type even though it is their “Building” scene because you are trying to inject into a Conflict scene? Or is the original Conflict scene over, and it’s only a +1 Ob at that point?
If the fight isn’t actually raging just yet, I’d go with:
Uncommon Occupation (I mean, come on) – +2 Ob, Outright proponent – +3 Ob, Opening to a Conflict – +1 Ob = total Ob 7 Circles test.
Good luck!
-L