
The Ragi |

Maybe.
Coup de Grace
As a full action, you can deliver a special attack called a coup de grace to an adjacent helpless opponent. You automatically hit and score a critical hit. If the target survives the damage, he must succeed at a Fortitude saving throw (DC = 10 + your level or CR) or die. However, if the target is immune to critical hits, the coup de grace does not deal critical damage or effects, nor does it force the target to succeed at a saving throw or die.
Helpless
You are bound, sleeping, unconscious, or otherwise completely at an opponent’s mercy. You are treated as having a Dexterity of 0 (making your Dexterity modifier –5), and melee attacks against you gain an additional +4 bonus (equivalent to attacking a prone target). Ranged attacks get no special bonus against you.
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During combat, against a fighting NPC? I wouldn't rule so. Against a hostage non-combatant NPC? Okay.

Yqatuba |

I figure it would mainly be something the badguys do. As for doing in combat I imagine it would be possible but would take too long to be practical, as I figure you would have to grapple and pin the person first plus coup de grace is a full round action so you would get hit by a lot of aoo and sneak attacks.

DM_Blake |

The OP isn't specific about the situation.
If two combatants are fighting each other in a combat, and one puts his gun against the head of the other and shoots, that's just an attack. No matter how you say it or describe it, trying to shoot a combatant is just an attack. That combatant will try to defend himself and therefore gets his full AC and all other defensive considerations and the attack will only be a critical hit if the attack roll is high enough to get one.
But, if the shooter has his gun against the head of an enemy incapable of fighting, then sure, a CdG is a good solution. For that to be compliant with the rules, the target needs to be Helpless. But there is some wiggle room for GM adjudication of exactly what "helpless" means. But it certainly means the "helpless" target is completely incapable of (or at least completely unwilling to) defend himself from the attack.
Per game rules, everybody gets to defend all the time. An invisible, silent enemy can sneak up on you while you're sitting quietly in a chair, reading a book, absolutely unaware of the undetectable enemy. But when that enemy attacks, he still must make an attack roll and you still get your AC. Surprise round? Sure. Flatfooted? Yep.
That's it. You're sitting down, reading, totally unaware of the silent invisible attacker. And yet, he still has to make an attack roll and you're flatfooted but otherwise perfectly able to defend yourself.
Not helpless.
No Coup de Grace.
So, even in that situation the defender can protect himself enough that he is not helpless and CdG is impossible, so it's hard to imagine any situation that is worse short of being asleep, paralyzed, bound, etc. (all the usual things that are clearly defined as "helpless").
Note: Pathfinder gives a bonus to invisible attackers but I didn't find that same bonus here. If Starfinder has it too and I just missed it, please let me know.
TL;dr: to answer the OP, no, holding a gun to the head of an enemy that wants to defend himself and is not literally helpless does not grant the ability to perform a Coup de Grace.

DM_Blake |

On a related note:
I've always found this to be somewhat disappointing for decades.
In a system with HP, where characters can get enough HP that they cannot possibly fear, or be intimidated by, or even respect a crossbow or a gun, the ages-old real-world scenario of pointing a weapon at them and telling them "Freeze or I'll shoot" is completely impossible.
They never freeze. They just don't care.
I know this game isn't "the real world" or anything like it, but the ability to threaten somebody with a loaded weapon, or a sword held against their throat, etc., is so iconic to our real world but it's completely missing in almost every RPG ever made.
So I personally would support balanced house rules to allow a Coup de Grace in situations like this, under the right circumstances.
I'm not sure what those house rules should be.
But it would be nice if an NPC could point a weapon at a PC and tell them to freeze and not have that result in the PCs laughing at the poor NPC fool before they kill him.

Pantshandshake |
My though is that basically any PC worth his or her salt is likely to be immediately identified as an Enemy Combatant, rather than A Suspect to be Detained.
The force continuum for a guy with a laser cannon in his hands and a grenade launcher attached to his armor probably skips past the ‘Police, put your hands up or I’ll shoot’ stage, is what I’m saying.
So for as much as it doesn’t work in a system where the damage from a single attack is generally laughable, it also wouldn’t make much sense for Officer Malloy to try and detain Bloodmaw, the Harbinger of Death from Vesk Prime. Especially on Officer Malloy’s last day before retirement. He’s really too old for this.
Which is essentially the same thing as hardbitten gang of whatever attempting to intimidate a starfinder party into putting their weapons down. Unless that gang looks like they’re a bigger threat than the horrors on Eox, they might as well be pointing a pistol at the PC’s and saying “Hi! Roll initiative!”

CeeJay |

There are narrative ways to make even high-level players feel the danger.
In Starfinder, the much-maligned gear chase also means that likely enemies and their weapons are levelling up along with the characters. Such enemies even in small numbers can still present a real and even deadly threat to a party.
Even if the guy in front of you is someone you could, all other things being equal, diss and dismiss, it's about more than the one gun in your face, the one sword at your throat: there is often something much larger behind them that the PCs still have to reckon with. If killing some random guard means getting into a war with an entire army, or an entire planet's law enforcement, or some far more powerful entity yet... even just the prospect of getting the more heavily-militarized units called in on them should give them pause. And they should have experiential reasons to have that pause.
It's a problem that can be solved with narrative and encounter-building as much as raw mechanics. You can of course build a system where, no matter how high-level you are, that one gun in one punk's hand can end you. Stars Without Number is your ticket, there... but baking that extent of "realism" into the mechanics can have serious drawbacks. It's certainly very hard to run that kind of system in the kind of heroic register that Starfinder delivers; SWN is very frank with GMs about the need for them to build the game around frequent character death, with combat something to be avoided at almost any cost.

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Well let's look at how the rules work, and see what the consequences are.
Case 1: the hostage is helpless
For example, tied up, or unconscious.
You can perform a Coup de Grace. You need to be adjacent, but it doesn't matter if you use a knife or a gun. The rules allow a Coup de Grace with either, just as long as you're adjacent and the target is helpless.
If combat has already started, you could ready an action to shoot the hostage if something happens ("they come towards me"). Note though that because it's not a purely defensive action, your ready action will resolve after their trigger. So if you're at only 1 HP, it doesn't really help to ready to shoot the hostage if they attack you. Also, note that shooting a helpless target is not an automatic success (unless you're performing a Coup de Grace). They do count as having a Dexterity of 0 though, so it's an easy shot.
If combat hasn't started yet, then it's going to be really important whether you win the initiative roll. If you win, then you can attack the hostage. If you don't, then the heroes get a chance to rescue the hostage before you can execute them.
Case 2: the hostage is NOT helpless.
He might be standing still for now while you hold a gun to his head, but he could start trying to dodge any moment.
You can't make a Coup de Grace because he's not helpless. While you're trying to shoot him, he's trying to dodge aside. This means you don't get your automatic critical hit. It means he might be fast enough to dodge, so you need to make an attack roll to see if you hit him at all.
---
Does it seem like it's too hard to stage a hostage situation? It's rather hard, yeah. But is that a bad thing?
In movies, hostage situations play out several different ways. Sometimes the enemy looks strong enough, and far away enough that the hero doesn't dare risk it. But in plenty of scenes, the hero has to make a decision - maybe he can take out the bad guy? Maybe if he distracts the bad guy his friend can sneak up behind him? Maybe he has to shoot the hostage through the shoulder so he can hit the bad guy right in the chest?
In Starfinder it's pretty rare for a single shot to kill a bad guy. So most of these cool movie moments would be impossible if bad guys could easily single shot hostages all the time.
If the bad guy's hostage killing is impossible to stop then all you can do in the scene is give the guy what he wants then that's pretty lame. If you have to time things just right and be smart and lucky as a player, that's much more exciting.
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Here's a couple of hostage scenes that would work in Starfinder:
* The BBEG has the PCs' mentor tied up and is holding a guy to his head while he negotiates with the PCs. If combat breaks out, he can do the Coup de Grace against the mentor as soon as he gets a turn. So the PCs need to make sure that doesn't happen. One of them could try to sneak up behind him and untie the mentor (no longer helpless). They could use Bluff to make him think they won't go for it and then maybe get a surprise round, and use Stellar Rush to bull rush the BBEG away from his hostage. They could just attack, hope they get lucky with initiative, and manage to shoot the BBEG dead before he gets a turn. Or hope they win initiative, run up to him and disarm his gun. If they win initiative, maybe they can use a Command spell to get him to drop his gun (if he fails his save). All of these are risky and exciting.
* Combat has been going on for a while and the ysoki PCs is pretty badly wounded (and let's say, out of resolve). Meanwhile a vesk melee PC is trying to get to the boss. The boss pulls out a really big gun and readies to shoot the ysoki if the vesk gets within 15ft. That's a mid-combat hostage situation. If the vesk risks it, then one shot from the boss might kill then ysoki before he gets close enough. Then again, the boss might miss.

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Do you want PCs and NPCs to regularly coup de gras each other, and that to be the most common and rewarded behavior?
Then yes.
Do you want the combat to go as expected with the adventure-themed rules of the game?
Then no.
I'm not at your table, and I truly hope you find the answer you and all the people playing with you enjoy the most.