The armed victim has the killer in her gunsights and at her mercy (it's usually a woman in these situations) but the killer knows they have nothing to fear. The victim is either unable or unwilling to use her weapon as the killer walks up to her and plucks the gun out of her hands leaving her a tearful heap begging for her life. Often involves a Breaking Speech. If she had captured him before hand or otherwise cornered him but doesn't shot then it's a Hannibal Lecture.
Compare You Wouldn't Shoot Me.
Examples:
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Anime and Manga
Occurs in One Piece, where Usopp's childhood friend Kaya draws a flintlock from her cloak and points it at her traitorous butler, who is the main villain of the arc. The butler recounts seemingly happy memories with her, takes away the gun, and dismisses all of those times as "endured" and "humiliating".
Double Suberted in Hellsing manga. Seras does fire her weapon at the vampiric priest - for all the good it does her. Then he disarms her.
In Planetes, Hachimaki is outrage at finding Hakimsabotaging the Von Braun mission, and trains an armor-piercing anchor gun on him. Hakim is utterly unfazed; he knows Hachimaki won't shoot, as he "doesn't have the eyes of a killer." He then delivers a devastating Breaking Speech at Hachi, steadily walking towards him. The lecture climaxes as Hakim walks past Hachi, who remains standing perfectly still, and barely has time to scream at his betrayer's back before a bomb goes off.
In Monster: Tenma has Johan at gunpoint, but hesitates. The latter calmly approaches the former in a way that suggests this trope... then he just stands there, points at his own forehead, and smiles.
Film
8mm: The Protagonist has the director of a snuff film tied to a support bar in the building the film was made at, has his gun trained on him... but can't bring himself to fire, even as the director taunts him (to the point of licking the gun). The hero then steps outside, calls the mother of the snuff film's victim, and begs for permission to kill the man. He gets it. Five seconds later he pistol-whips the director to death.
One of the few tropes played straight in Last Action Hero, when Danny repeatedly has villains at his mercy but can't pull the trigger. Understandable, since he's a scared kid, and we wouldn't want him to become a killer anyway.
Variant in Disney's version of Tarzan: Tarzan doesn 't fire the rifle because he can't figure out how to make it fire.
The Host: The heroes are not afraid to shoot. They're just (mostly) shitty shots. Add to that one of the characters, a national bronze-medallist in archery, has a nasty habit of hesitating before taking a shot, and you know the monster has nothing to worry about. Hence why it charges the main characters at every available opportunity.
Subverted in Wolf Creek. However, it doesn't kill the villain: the rifle bullet passes through his neck and somehow he doesn't bleed to death.
The Rock: Just after Goodspeed and Mason's Navy SEAL teammates are all drawn into a trap and killed, Goodspeed tries to stop Mason from leaving Alcatraz Island by pulling his pistol on him. Mason replies that Goodspeed doesn't have what it takes to kill him, and also remarking "Besides, the safety's on", before grabbing the gun away.
A rare good-guy/good-guy example occurs in Independence Day, as Major Steven Hiller is climbing into a helicopter to go look for his girlfriend:
NCO:Hey, what the hell you doing? (Draws pistol, points it at Hiller) Get out of there, sir.
Hiller:Something I gotta do. I'm just gonna borrow it for a while.
NCO:No you're not, sir.
Hiller:You really gonna shoot me? (NCO hesitates, and then lowers the gun.)
Hiller:Just tell 'em I hit you. (the [rather large] NCO looks insulted as Hiller takes off.)
In The Sound of Music, Rolf becomes a Nazi soldier, but proves unable to kill Captain Von Trapp:
Captain Von Trapp: You'll never be one of them.
Parodied in National Lampoon's Loaded Weapon 1, where a character seizes up and -rather than merely trembling- begins to convulse in an exaggerated manner, wagging his pistol in every direction. Said character, by the way, is played by Samuel L. Jackson.
Played straight in The Ref. In it, Denis Leary gets distracted, leading to the son of his two hostages grabbing his gun and demanding that Leary untie his parents or he'll shoot. However, Denis knows the kid's not a killer, and starts moving towards the kid. When the phone rings and momentarily distracts the son, Leary simply takes the gun back.
In Die Hard With A Vengeance Zeus (another Samuel L. Jackson character) is holding up the entire bad guy parade with a gun, at which point Simon Gruber walks up to him, promptly explains that Samuel L. Jackson of all people forgot to turn the safety off, then captures him.
Literature
In the Discworld novel Jingo, eccentric inventor Leonard of Quirm has captured Sgt. Colon and Corporal Nobby using a firework missile and a rifle mechanism he invented. He then stops, hands the pieces of his weapon to his captives and proceeds to redesign it on the spot. The two ex-captives simply fire the incredibly inaccurate weapon. Hilarity Ensues.
Oddly featured in Nation where Daphne points a gun at Mau. She seems so scared of it that he tries to take it from her to relieve her concern. She does actually fire it, but fortunately the powder had got wet, and he thought she was giving him a tool for lighting fires with. So easily could have been Poor Communication Kills.
Subverted in one of the Track novels (by Jerry Ahern) when a neo-Nazi gives his revolver to a nun and dares her to pull the trigger. Of course, since the nun is the heroine in disguise he gets shot between the eyes instead.
Svidrigailov and Dounia in Crime and Punishment by Fyodor Dostoevsky. Dounia has a defensive failure in front of Svidrigailov while Svidrigailov attempts to disarm her, laughing at her and taunting her to kill him. She doesn't, of course.
A small but memorable scene in one issue of Perry Rhodan has Pyon Arzachena, perpetually down on his luck interstellar prospector, threaten the formergalactic conqueror Hotrenor-Taak with his own weapon because he suspects the latter of being merely an impostor whom he wants to unmask. Turns into a Not With the Safety On, You Won't moment when Hotrenor-Taak calmly walks over and retrieves his gun — which only works when held by its owner.
Real Life
Reportedly happened when Fidel Castro's lover, Marita Lorenz, tried to assassinate him.
Spectacularly averted by the recent case of one Rukhsana Kauser in Kashmir. When six heavily-armed men burst into her home and began beating her parents, Rukhsana and her brother attacked the men with axes; Rukhsana stunned the bandits' leader, snatched his AK from him, shot him twelve times, then she and her brother drove off his surviving accomplices after a protracted firefight.
The possible reality of this trope is why all decent mandatory gun safety courses will emphatically point out that if one has drawn the gun and taken aim, they must immediately use it to shoot the aggressor(s) until they fall down. On such a gun safety test, mentioning that one would consider using the gun as a threat is grounds for immediate failure.
To elaborate a bit further, DO NOT BLUFF with a weapon. A person who is used to killing people (i.e. most violent criminals) will kill you right then and there if you pull out a weapon and don't attack immediately. Unlike you, they have no resistance to killing. This is where Hollywood sort of gets it right and sort of gets it wrong—a lot of people get killed by waving around a gun they're not prepared to use, but the killer rarely bothers to disarm, taunt, or otherwise interact with the victim before murdering him.
Also, depending on your jurisdiction, it may be legal to shoot someone in self-defense, while at the same time being illegal to brandish a weapon, which is to say, displaying it openly or threateningly. Which means, due to an odd intersection of laws, once you draw the gun in self-defense, it is illegal not to use it. Of course, firearms laws vary from place to place, in the case of the US, they vary wildly between individual states, so become familiar with your local laws and act accordingly.
Live Action TV
Occurs in the pilot of Angel, except the gun wouldn't have stopped the vampiric villain. Not that the victim knows that.
In an early episode of Stargate SG-1 Samantha Carter has an ex-lover at gunpoint as he has been suffering delusions of grandeur. He even tells her to shoot him but she still cannot.
Lampshaded in an episode of Doctor Who - Martha has an enemy at gunpoint who says she doesn't have the nerve to fire - she replies that nervous people with guns are not a safe combination, and asks him if he wants to risk it.
And reversed in an earlier episode. The Doctor is holding a man at gunpoint. He being the Doctor, he handles it differently when the man starts getting nervous...
Doctor: Like I was ever going to shoot [throws him the gun]. So you were saying?
Man: But...I've got your gun?
Doctor: Okay, so shoot me. You were saying?
Man: Well, uh...can I put this down?
Doctor: If you want, just hurry up.
But played straight in "Utopia" when Chantho won't shoot Professor Yana even though it's pretty clear at that point that he's become The Master.
And played straight in the Doctor's Daughter where Ten makes a point that even if he has the villain at gun point, he never would shoot.
In another episode, a scared kid genius has the Doctor at gunpoint. The Doctor just sighs and simply takes the gun barrel, complaining about humans and guns.
Happens to Amy Pond in Cold Blood.
Subverted in "The Doctor, The Widow And The Wardrobe". The titular widow manages to trick a group of soldiers and turn a gun on them. The leader tells her that he doesn't believe she'll shoot. Then she informs them that her children are missing. He takes her much more seriously after that.
Subverted on Lost: Kate is in a bank during an armed robbery. After a skirmish, she ends up holding a gun on the ringleader, but the safety is on. As the other hostages call out to shoot the bad guy, she yells, "I don't know how to use a gun!" The bad guy takes the gun back and drags her into another room, ostensibly to beat her up. That's when we learn that Kate masterminded the bank robbery, is playing the inside woman, and most definitely knows how to use a gun.
Variation in the British anthology series Thriller: the heroine tries to phone the police, but the villainess cuts the phone wire and proceeds to threaten the heroine. At which point the heroine is so shocked that she drops the telephone receiver, never stopping to consider that it's a heavy blunt instrument with which she could have clouted the villainess.
Wendy Patrakas falls victim to this on Drive. She's assigned to shoot Ivy to stay in the race. However, street smart Ivy easily disarms the Ohio housewife. After seeing what Ivy's capable of, Wendy tells her "I think maybe I should've shot you."
Crichton's Love Interest in Farscape falls victim to this. Scorpius holds Crichton hostage. Then the Love Interest confidently walks in with a pulse rifle. Crichton laughs and tells her to shoot Scorpius. She then hesitates, and Scorpius calmly shoots her instead.
Video Games
Happens a couple of times in the Metal Gear series
In the first game Meryl points her rifle at Snake, and Snake taunts her about not being able to pull the trigger
Subverted in Snake Eater, near the beginning when Ocelot points his gun at Snake, Snake laughs and says "You don't have what it takes to kill me." An enraged Ocelot pulls the trigger, only to discover that his gun is empty. Whoops.
There are implications that Ocelot intended for this to happen all along.It's hard to maintain an image of being a Russian soldier if you refuse to shoot an American spy, after all. Emptying your weapon beforehand is a nice third option.
Subverted in Lucas Arts FPS Outlaws. When he was a young boy, the hero was in this situation, holding the gun, trying to save his father, but failed. At the end of the game, he is one staring down the barrel, but is saved by his daughter.
Happens in Grim Fandango when Meche threatens Domino with a Sprouter.