Cowboy Bebop: death is the only way to leave the crime syndicates. Especially the Red Dragon.
In Crying Freeman, The Freeman got abducted, then forced to work as an assassin for the Sons of the Dragon and obviously he isn't allowed to leave them as they initiated him against his will in the first place.
In Noir, the secret organization Soldats has absolutely no problem assassinating people who used to kill for them.
Implied in the climax of Jin-Roh: The Wolf Brigade. After the protagonist Fuse shoots dead his Love Interest, we see another member of the unit in a nearby derelict building, de-cocking his Broomhandle Mauser which he had aimed at them.
Akatsuki in Naruto. As Konan unfortunately finds out.
It's quite a bit more complicated than that...it's more like the new administration was running counter to its original goals and thereby disgusted original members like Konan.
In Death Note, at the Yotsuba group's "meetings of death," one member, Hattori, gets scared of going to jail and says he wants to quit the meetings. After Higuchi warns him that a statement like that might get him killed and Ooi reminds him that he's too deeply involved to escape blame, he apologizes and retracts his statement, but later gets killed anyway.
In Bakuman。, writers cannot simply end their series when they want to, as long as there's still some life in the series, and if they simply abandon their series, they will never be able to write for Jump again. Mashiro and Takagi manage to secure a compromise in which they quit their current series to launch another that can compete with Eiji's works, and Eiji himself cancels his own series after becoming the most popular manga artist in Jump.
Soul Society Captains in Bleach. You don't get to just step down and go on about your day. If a Captain "Retires" he either died in combat, got Kenpachied or is locked away in prison.
Or they got promoted into Squad Zero. Or just up and left without permission, as in the cases of Yoruichi and Isshin, which presumably results in them being considered fugitives.
A standard in evil organizations (see Hydra for Marvel Comics) and villains' mooks. No one can leave The Joker's gang alive, or the Red Skull. Even Always Chaotic Evil races are so: Skrulls (Marvel Comics) are said to be euthanized when old. Ninja clans in particular are notorious for this rule.
The Hand is especially nasty, since they can raise the dead. Even death isn't an escape.
Less sinister version in Ex Machina. During a crisis, Mitchell's second-in-command starts saying he's going to quit, only for Mitchel to interrupt forcefully and say he needs him because he needs someone questioning him every step of the way, even if he can't always agree.
Late in The Seventies, the Marvel villain the Purple Man had a Cut Lex Luthor a Check epiphany. He realized that he didn't really need to be a supervillain to get what he wanted, because he had a Compelling Voice (actually, super-pheromones, but it works the same), so people would just hand him whatever he wanted, and thank him for the privilege. So he tried to quit being a villain and take up a life of hedonistic debauchery. Cue almost a decade of stories in which some Big Bad (like the Kingpin or Doctor Doom) would track him down and force him to help with their latest Evil Scheme. Since then, he's apparently become resigned to his fate, and his last several appearances have shown him trying to Take Over the World.
Nextwave sees Dirk Anger contemplating/attempting various suicide methods. He eventually succeeds in hanging himself...accidentally, but to his annoyance, Beyond Corporation did not accept the terms of his retirement and brought him back as a zombie. A green one, who craved brains. It's that kind of series.
Monica's Gang: A story featured three scientists who worked developing weapons for a Corrupt Corporate Executive. When they decided to quit, he kept them locked in the lab and said he might accpet their resignations fifty years later. The scientists escaped.
The President's Analyst: Sidney Schaefer believes he will not be allowed to resign since he knows too much about the president. After a paranoia induced dream he deserts and is pursued by people who want him dead or captured. 
Kill Bill: When The Bride tried to resign from the Deadly Viper Assassination Squad, they tried to murder her. She did make it look like she cheated on a professional hitman, so it might be something other than she knows too much.
The second installment indicates that she didn't quit as much as walk off her current assignment and allow Bill to think that she was dead so that she could avoid having him raise their child as an assassin, although it's likely that quitting normally was not an option.
It was more like Bill was pissed off at having his girlfriend dump him for no apparent reason and shack up with a record store owner in the middle of nowhere, who mistakes him for her father.
Bill: There are consequences to breaking the heart of a murdering bastard.
Averted in Men In Black, where the technology to alter people's memories means an agent can retire without the agency worrying that He Knows Too Much. Although the second movie shows that it's possible for the agency to find an ex-agent and restore his or her memory if needed, which verges into Mandatory Unretirement (if things get to that point, they're not going to take no for an answer).
Fitz-Hume: Ah, Colonel we were just talking and uh we've had loads of fun here... and uh you know we met new friends... and had a great lunch... wasn't that a great lunch? Milbarge: Yah, the tuna and cream caserole was beautiful. Fitz-Hume: ...Was great! And uh, anyway we were just talking and we'd like to go home now. So uh thanks for the bruses and you can keep the stool samples... Col. Rhombus: Boys... it'd be a shame to have to kill you now.
The entire plot for Operation Endgame at first seemingly revolves around setting up a situation where all prospective defectors and/or resignors are tasked with killing one another.
Big Boy: You are not out! When you are dead, then you are out!
Aubrey Maturin: Secret agent Duhamel falls victim to this when trying to defect.
From the Harry Potter series, the Death Eaters are this sort of organization.
Sirius (talking about his deceased brother): From what I found out after he died, he got in so far, then panicked about what he was being asked to do and tried to back out. Well, you don't just hand in your resignation to Voldemort. It's a lifetime of service or death.
In her case, though, it's more of a fear of a Face Heel Door Slam than this trope. Leaving wasn't the problem—well it was, but she could handle it—being accepted by the new team was, as she was technically guilty of treason for her previous acts. After The Reveal, she's forced to go back to Zsinj. She proceeds to sabotage Zsinj's efforts from the inside. Afterward, she ends up Faking the Dead, creating a "new" identity for herself—actually a very old identity, but now on a more permanent basis—and hooking up with Myn Donos, who by this point had forgiven her for destroying his squadron.
"After every major victory, I hope the fighting is over, but it'll never be over. Even after we defeat the Imperials, there will be someone... another threat to peace..."
Subverted in another book of the X-Wing Series, when Warlord Zsinj mentions that it's about time for one his subordinates to retire. Face Loran, impersonating another of Zsinj's subordinates, asks if he should take care of that himself.
"I meant an actual retirement, Zurel. He goes away to live in a cottage somewhere and writes his memoirs."
Wedge and Tycho keep trying to retire and always end up getting called back by the next Really Big Galactic Crisis. They're getting older.
Wedge: "We keep trying to retire. Give up this life of shooting things." Tycho: "We're really men of peace at heart."
Uli Divini was a genius teen surgeon during the Clone Wars who had enlisted for one tour, after which he would go back to his homeworld and presumably start or join a practice. Instead, since the new Empire was short on doctors, they executed an Imperial Military Stop Loss Order, or IMSLO. As a result of that, Uli served for twenty years, getting rather jaded in the process. He tends to Princess Leia after she is tortured, and since he seems like a pretty decent guy she demands to know why he still works for the Empire; he tells her that he can't leave, he'll be shot. He joins the Rebellion when the Death Star is destroyed, somewhat to his own surprise.
(IMSLO is) A retroactive order mandating that, no matter when you'd been conscripted, once you were in, you were in for as long as they wanted you - or until you got killed. Either way, it was kiss your planned life goodbye. Imperial Military Stop Loss Order. An alternative translation, scrawled no doubt on a 'fresher wall somewhere by a clever graffitist, had caught on over the last few years: "I'm Milking Scragged; Life's Over."
Years before Galaxy of Fear, Mammon Hoole worked for the Empire in a lab. When something went horribly wrong and a world was cleansed of life, his lab partner stayed with the Empire and profited significantly from it. Hoole left, horrified, and found himself blacklisted by the Empire and blamed for the disaster. He had to drop part of his name.
In Catch Twenty Two the main characters have to fly a certain number of missions before they are discharged. The number of missions keep increasing however...
The Firm: This is a defining characteristic of the titular firm, Bendini Lambert & Locke.
If you're an agent of the Laundry in Charles Stross's The Laundry Series you can't quit. Ever. In fact, you probably weren't even given much choice in joining — most Laundry agents were too close to unleashing Eldritch Abominations by accident and simply weren't safe to leave in civilian life. If you screw up they'll put you on unimportant duties but they can't fire you for the same reasons. It's strongly hinted that Laundry agents don't even get to quit once they're dead.
In The Dresden Files, this is how Lara Raith treats her employees. After several of them are crippled/fatally wounded in an attack by an Eldritch Abomination, she orders her people to take them to her (life-force sucking) sisters, who are also wounded. Harry protests, knowing that if the sisters feed on those people, the people will die. Lara calmly states that they know too much about the White Court to allow them to be let go, and that with the sheer severity of the injuries sustained, their quality of life is borderline nonexistent. Harry, naturally, finds this to be reprehensible, and Lara retorts that he seems to have forgotten that she's a monster. A neat, habitually effective, incredibly efficient monster.
Vladimir "Viktor Suvorov" Rezun, a defector from the GRU, Soviet military intelligence, started Aquarium, one of his books on the subject by reminiscing about how he was told, when joining, "Theoretically there's only one way out for any member of the organization—through the chimney of the crematorium." And then the recruiter showed him a film of somebody who tried to leave being put into the furnace alive. note When questioned, he says "I don't know if the film's real, but I was shown that".
The Dark Forest from Warrior Cats. In The Last Hope, Beetlewhisker tries to leave, but Brokenstar kills him.
In "A Song of Ice and Fire" you have both the Kingsguard and the Night's Watch. Both requires an oath to join, and once that is said, there is no way out. If you desert, they will hunt you down and kill you. The exceptions are Ser Barristan Selmy and Ser Boros Blount of the Kingsguard, but both of those got fired rather than resigned, and those are the only examples in recorded history where this has happened.
Live Action Television
Babylon 5: once a psychic is conscripted into the Psi Corps, they are not allowed to leave. Anybody who does leave is hunted down and executed. The telepaths who take sleeper drugs are sometimes killed or commit suicide.
The Prisoner is based entirely around this trope. Possibly excepting the last episode.
Heroes — the shadowy Company started by "the 12" doesn't like quitters. One guy does manage to quit, but he has the advantage of being invisible.
He still had to fake his death to do that.
In the 1970s The Bionic Woman episode "On the Run" (the final episode of the series), Jaime Sommers tries to resign from the OSI but discovers that if she does so, she'll be confined to a government compound for the rest of her life. (This storyline was inspired by The Prisoner.)
The Pretender: The Centre won't accept Jarrod's resignation although he doesn't exactly try and stay below the radar after he escapes. Plus he was never an employee, only a company asset.
Alias: Sydney Bristow tries to quit SD-6, The C.I.A. and just about any other intelligence agency, even being called back into action in the series finale, after achieving ... Happily ever after isolated on a remote island
UFO: In "Kill Straker!", Colonel Foster is subject to alien brainwashing. The others contemplate killing him because He Knows Too Much about SHADO, and therefore can't just be fired.
In The Fixer, John Mercer can either work for Lenny Douglas or go back to prison.
Chuck thinks he's free to leave the CIA in the second season, but he would have been assassinated by his own handler had he actually quit. As of the fourth season, Chuck's attempts to find a job outside the CIA after being given explicit permission to leave are foiled by the CIA, which is apparently willing to go back on its deal with Chuck and blackmail him into working for them again.
In Angel, the evil law firm Wolfram and Hart doesn't just have its employees sign contracts that are in effect until death, they extend beyond the grave.
Defied on The Wire. Cutty returns from prison and joins Barksdale's crew (Avon having recruited him in prison). After he can't pull the trigger on an enemy Mook, he apologizes to Avon, saying "The Game ain't in me no more" and clearly expects to be killed in response. Avon lets him go with a Man Hug.
Slim Charles: He was a man in his time, y'know? Avon: He a man today. He a man.
In 30 Rock Jack learns that the Bush administration is doing this, forcing him to instead lead a costly, embarrassing, and useless military research project to get fired.
Sort of. Late in the second season of Nikita, Percy admits he's tired of the whole conflict and offers Nikita a deal to make Division leave her and her crew alone if they just stop interfering in Division operations. Nikita turns it down, as she refuses to let the fight end on anyone's terms but her own — after all, she's in it to save the world.
Several episodes of Get Smart dealt with CONTROL protecting defectors from retribution form their old employer KAOS.
Averted with the Tanglewood Boys gang from CSI: NY. The Tanglewood Boys seem to be precisely the sort of group that this trope would apply to, but the official gang tattoo includes room for two dates: the date when someone joins the gang and the date when he leaves it. And while Danny says that leaving the gang alive "hardly ever happens," the show gives at least one example where it did: Danny's brother Louis.
Pretty much every evil organization in Feng Shui is like this. The Ascended are particularly ruthless in this regard when it comes to their Pledged pawns.
Common behaviour for the clans and sects in Vampire The Masquerade, since they really don't want their secrets leaking out to enemy factions.
The Tau's Fire Caste (the military). There are only two ways to get out: death, or by opting to take a third "trial by fire" (the first two are given to all Fire Warriors), after which they are allowed to become military advisers instead of continuing to fight.
While some Imperial Guard regiments have a fixed length of enlistment, others are more like this; some literally keep fighting until they are too depleted to be useful, then muster out all survivors, while others let enlisted men retire only at periodic reorganisations, while taking reinforcements at all times. Depending on when he joins, a soldier in one of these may serve for two years or twenty. Officers have a more defined idea of retirement age, but talented ones may be called back into service when necessary.
Kingdom Hearts: Organization XIII operates this way. Marluxia, Larxene, Xion, and Roxas all have Axel, the group's official assassin, sent after them when they go rogue. When he eventually turns traitor, too, second-in-command Saïx comes calling. The Trope Namer is a line spoken by Saïx to Roxas when he tries to stop Roxas leaving the organization for good. Saïx is beaten by Roxas in battle and Roxas defects from the organization.
Deus Ex. The biggest downside of all that neat nanotechnology you have is probably the kill-switch no one told you about that can be activated if you ever decide to change sides.
The story in the original Bushido Blade states that the player's chosen character is part of a small assassin cell that has a "You only leave when you die" rule in place. They want out.
Eternal Champions has Shadow, who was part of an assassin agency. When she found herself sympathizing with their victims and unable to kill anymore, she threw herself off the roof of their headquarters - they gave her no other way to leave.
Shadow Warrior's Excuse Plot has Lo Wang quitting Zilla Enterprises after learning of his employer's plans to rule Japan using creatures summoned from the dark side. Master Zilla decides to use said monsters to kill Wang. Much ninja asskicking ensues.
Salem: "The Lopto order does not tolerate traitors. That's the rule..."
A City of Heroes story arc involves a Crey employee who wants to move out of Paragon City with his wife. They go to some extrememeasures to try to keep that from happening.
Part of Taki's All There in the ManualBackstory in the Soul Series. In order to leave Japan and investigate Soul Edge, she has to abandon her ninja clan. One of steps involved in doing this is fighting her pissed-off master, who wanted Soul Edge for himself.
The Sith on Manaan in Knights of the Old Republic has a double subversion. The young Selkath who are being trained as Sith claim that one who wanted to leave was allowed to do so, but if you look a few rooms over, you find him dying, and this convinces the Selkath to run away.
In Dragon Age: Origins if an Antivan Crow like Zevran fails an assassination he/she is considered dead to the Crows. Some Crows like Ignatio are willing to merely pretend the errant Crow is dead. Others want to make absolutely sure that is the case one way or another. If the Warden lives, Zevran will tell him/her that he knows the Crows will keep coming after him and that he will keep on fighting them for his freedom which is canon in Dragon Age II. If the Warden dies, Zevran will return to Antiva and take over the organization. It is both a victory and a defeat. Zevran has his life and a position of power and influence — but he never truly escapes the Crows.
The Grey Wardens themselves aren't big on people walking away from them, although even if you try, you still have the taint in your blood and a sharply reduced lifespan before the "last walk".
Mass Effect 3: This turns out to be the case for anyone who decides to quit after joining Cerberus, including most of your crew from the second game. A number of missions center around helping various former team mates fight off Cerberus retribution, and at least one former crew-mate's survival relies entirely on a dialogue choice when you first run into them in the third game.
Kevin & Kell: The cult in The Wild. Rudy is forced to recruit for them at an airport, watched by several agents who plan to eat him if he attempts to run away. Kevin manages to sneak him past the agent at the exit by disguising him as his seeing-eye dog. On the other hand, when Ralph joins and never amounts to anything, the pack doesn't try to stop Kell from retrieving him.
The Order of the Stick: When Haley quits the thieves' guild, the leader, Bozzok, gives her a head start before the ditzy-but-powerful assassin Crystal is sent after Haley. Of course, she has to reenter Greysky City later in the story. Like the thieves guild rules say "You can only leave in a coffin. And vampires can't even leave in one of those."
Non-lethal version of the trope in Rival Angels. Anybody who tries to quit working for Yvonne Carmichael (Damage Inc's leader) before she feels like firing them has at least one severe ass-kicking in their future. The York Sisters and all three members of The Syndicate learned this the hard way.
Justice League: Task Force X — better known as the Suicide Squad, though they couldn't use that term on a kids' show. At the end of the episode of the same name, the criminals think they're done after one mission. Nope... they've got a long time to work off their sentences. They're let off once the parent organization (Cadmus) is disbanded at the end of the season.
Justified due to the fact that you couldn't simply quit if you were drafted into the military. Pete's threatening of Donald is also justified due to the mentality present during World War II - not helping the war effort and doing your patriotic duty was tantamount to aiding the Axis.
Stop-loss policies in the military allow the army to keep you in it past the time you agreed to enlist for and can even stop you from transferring to somewhere else.
Not entirely true. They can recall you to active duty for a time after you are discharged from the service, but the period of time in which they can do so is spelled out in the enlistment contract. During that period of time, you are considered to be a member of The Reserves.
This is quite standard for criminal gangs and syndicates the world over. Once you join a criminal organization, you're in it for life, and the only way to leave it is in a body bag.
Prison gangs in particular have a "blood in, blood out" policy — joining the gang frequently requires spilling the blood of someone from a rival gang (blood in), and once you're in the gang, the only way out is death, either at the hands of the gang or at the end of your natural life (blood out).
Some countries forbid their heads of state to quit office, even if it's the only thing they can ethically do. The closest example of this trope is Mexico, since the Mexican Constitution states the only way a Mexican president can be able to quit office is being judged for federal crimes (like high treason) or dying due to natural causes or accidents. This law was created after the Mexican Revolution for preventing a president to quit so easily and for avoiding a coup d'etat.
Actually, (according with Wikileaks) there is a way for a Mexican president to quit office, but implies suspending the Constitution (so any laws regarding the presidential mandate will become void), and no Mexican president will resort to that, even in the most direst circumstances, since it could be used against the president itself in any time.
Technically the case for Members of Parliament in Britain. A rule dating from the time of James I forbids resignation from the House of Commons. In those days, being an MP could be quite a hassle, especially for those representing rural constituencies far from London: you couldn't handle personal business back home and the trip to and from Westminster could only be conducted by poorly-maintained roads. And it was at the time not unusual for an MP to be elected involuntarily, providing further incentive to quit. As a result, the House passed a rule barring its members from resignation. However, as part of the Act of Settlement 1701, anyone holding an "office of profit under the Crown", i.e. a paid job in the executive or judicial branches of government, was disqualified from Parliament unless re-elected in a by-election; the English Civil War had made Parliament wary of royal influence on the Commons, and wanted to keep the king from controlling MPs by giving them jobs (if an MP's income depends in part on the king, he might be trusted to vote the king's way). This had two effects:
Until the early 20th century, any MP appointed to the Cabinet—including the Prime Minister—had to seek re-election in his constituency in order to hold the seat and the office. At first this wasn't a problem, since most Cabinet members were Lords anyway, but as the number of members of the Commons in the Government rose, an exemption was made for certain situations.
One could once again indirectly resign from Parliament by taking a paid office under the Crown. Eventually, it became the custom to take the office of Steward and Bailiff of the Chiltern Hundreds or the office of Steward and Bailiff of the Manor of Northstead, which had been sinecures with piddling pay for generations, as the means of resignation from the House. This has become so common that someone taking these offices is simply said to have resigned from Parliament in daily speech and the press.
In an amusing incident, Northern Irish Sinn Fein leader Gerry Adams, who had been an (abstentionist) MP for Belfast West since 1997, decided to resign Parliament in 2011 to seek election to the Dail Eirann. When he won a seat at Leinster House, he submitted a letter of resignation to the Speaker but didn't apply for a Crown office, as he is opposed to the monarchy on principle. The Chancellor of the Exchequer's office (which handles these things) sent him a letter apologising and saying, essentially, "sorry, there's no other legal means for you to retire from the Commons, so here's your commission and your cheque for the pittance we technically have to pay you".