Poisonous Captive

Captured doesn't necessarily mean cowed. A Poisonous Captive is a villain held prisoner by the heroes who continues to undermine their objectives through their toxic influence. They have a tendency to spark disagreements between allies (up to and including the spread of a Hate Plague), to shake the good guys' confidence in themselves just by talking, or just to make them feel uneasy by virtue of being closer around than they were as a free agent. Despite the heroes' best efforts, it's usually difficult to keep the villain in the dark about everything that's going on or prevent them from divining weak spots, so the longer they're held the more of a danger they pose, especially should they escape—meaning it's all but inevitable that they will.

Particularly dangerous cases may pose the threat of a hero's untimely corruption, if they start listening to the villain's cynical-but-persuasive advice, buying into their justifications for evil deeds, or being tempted by offers made in exchange for freedom.

Another common scenario is that the villain is held secretly, meaning that if word were to leak out, the captors run the risk of getting in serious trouble with their superiors, being deposed by their inferiors, or losing PR with the general populace.

Makes a pretty good case against Thou Shalt Not Kill, but the typical reason for keeping him around is that the villain has some kind of information the heroes need desperately enough for it to be worth the risk. In some cases, murder would be counterproductive or even impossible, if the captive is immortal.

May be a result of I Surrender, Suckers. Compare Pity the Kidnapper, a comedic version (which usually involves villains as captors rather than heroes), Might as Well Not Be in Prison At All, and Sealed Evil in a Can. The inverted, heroic version often falls under Talking Your Way Out.

Examples of Poisonous Captive include:

Anime and Manga

Fullmetal Alchemist has Envy, when he was trapped in a flask. He was able to play on May Chang's fear for her clan and talk her into going back instead of taking him to Xing, which allowed him to get free and obtain a second Philosopher's Stone.
Soul Eater's Medusa, for the brief time she was imprisoned, did absolutely nothing for Crona or Maka's peace of mind.

Comic Books

The Thing Behind the Wall in Johnny the Homicidal Maniac. Nny has to keep it trapped by keeping the wall covered in fresh blood, which naturally does wonders for his already fragile sanity. Then the Thing gives two Styrofoam dolls in Nny's apartment sentience, the idea being that they'd persuade him to commit suicide and thus release it.

Film

In U-571, the German submarine prisoner continuously causes problems for the American crew, until he is killed.
In the aptly-named movie Suicide Kings, a bunch of amateurs kidnap retired mafia boss Christopher Walken for somewhat convoluted reasons. Needless to say, Walken turns them all against each other in record time.
Teaching Mrs. Tingle essentially uses this as a plot framework.
In The Dark Knight the imprisoned Joker manages to blow up the jail and works on a cop's psyche until he breaks out.
Ruthless People at first, till it turns into A Match Made in Stockholm.
In the film Southern Comfort, the National Guardsmen capture a one-armed French-only speaking local Cajun hunter and trapper, one of the Cajun's who were threatening them. They attempt to talk to him but he only speaks French. Nevertheless, just his presence is enough to poison the group.
In the remake of 3:10 to Yuma, Ben Wade kills off his captors one-by-one as he's transported to the train station. They're all too nice to plug him on the spot.
In The Avengers movie, Loki gets captured quite early on. Despite the team's best preventive efforts, it ends spectacularly poorly.
Hannibal Lecter is at least the Trope Codifier if not the Trope Maker in regards to film.

Literature

In The Wheel of Time, the heroes captured no fewer than three Forsaken individually, and between them they covered just about all of the risks inherent to this trope. Asmodean was (sort of) on Rand's side, so the danger he posed was mostly just if word got out about who he really was, but you have to question the wisdom of keeping around a character like Semirhage.
- Nor was that the first instance of Semirhage fulfilling the trope. During the War of Power she was once captured by the forces of Light. By speech alone she terrified her guards so badly that they smuggled her out of captivity rather than face the tortures she threatened them with.
Hannibal Lecter. Not for nothing was he the Hannibal Lecture's Trope Namer.
The Silmarillion. Sauron ended up corrupting and destroying the Numenoreans after they captured him.
In The Three Musketeers Femme Fatale Milady de Winter pulls this by seducing her jailer when captured in England, twisting the guy so much that he becomes an assassin, attacking The Duke of Buckingham (also a Historical In-Joke, as this event really happened).
In the Second Apocalypse series, Anasûrimbor Moënghus during the time he was a prisoner of Cnaiür urs Skiötha's tribe. He seduced Cnaiür's mother, convinced Cnaiür to kill his father, and talked Cnaiür into setting him free.

Live Action TV

Spike tended to be this when held by the Scoobies in season four of Buffy the Vampire Slayer.
In Angel season 4 Angelus did this to the crew of Angel Investigations.
Ben from Lost makes his first appearance as the captive "Henry Gale", and spends his entire time in captivity playing mind games with the survivors and attempting to turn them against one another.
Nate Haskell (Bill Irwin) on CSI.
Simeon on Stargate Universe.
A Silurian warrior woman in series 5 of Doctor Who . She managed to convince one of the people guarding her to act on her worst impulses.
Sylar to Mohinder in the Heroes episode "Parasite."

Video Games

In Metal Gear Solid Peace Walker the player can capture Zadornov and keep him in a cell in an attempt to convince him to join your cause. Ultimately, he breaks out numerous times and goes into hiding, forcing Big Boss to waste time locating and recapturing him each time. Each time he escapes, he's been released by Paz, who's using him to divert attention while she makes modifications to Metal Gear ZEKE.
The entire premise of Arkham Asylum.

Web Comics

Hands down, Cyndi from Penny and Aggie. She manipulated her captor into attempting suicide. What's not poisonous about her?
This was Faden's entire schtick in Exiern. He was captured a couple of strips in, spent almost the entire time in captivity and still proved to be an effective villain.

Western Animation

The Joker on the Batman: The Animated Series episode "Mad Love", who was able to talk his psychiatrist Harlene Quinzel into becoming Harley Quinn while still in Arkham. And it was implied early in the episode that he compromised the ones before her in a similar fashion.
- Batman himself has also done this to teams that the Joker has been on (though the Joker saw it coming).
Batman also does this in Justice League, when captured by Lex Luthor's villainous team. He bribes Ultra Humanite to save the Justice League from Luthor's plan and take down the team from the inside, frames the perfectly innocent Cheetah as his accomplice, drives a wedge between team members and generally makes a nuisance of himself, all while restrained. And then, as the kicker, reveals in the climax that he could have escaped at any time but stuck around 'to keep an eye on' the Injustice Gang.