Fakeout Escape

Say you're trapped somewhere with no possible means of escape. All you have to do to get out is make it look as if an escape has already happened. Then your guards' attention will turn to figuring out how it happened, re-establishing a perimeter further out to contain it, and that sort of thing, and you can make your escape for real.

In one common version of this, a prisoner in a cell hides somewhere (behind the door, using a Ceiling Cling, or the like). The one inept guard thinks they escaped and opens the cell, and the prisoner either knocks them out or locks them in.

Compare Decoy Hiding Place.

Examples of Fakeout Escape include:

Anime and Manga

In Dragonball Z, Vegeta is imprisoned inside a healing tank on Frieza's ship. When he breaks out of the healing tank, it alerts the guards. So he blasts a hole through the wall to make them think he has escaped the ship; while Frieza's henchmen are searching for him outside the ship, he takes the opportunity to go steal some dragon balls and then escape.
In Durarara!!, Shingen fakes Celty out by sending the elevator to the bottom floor while he hides. He then tries to make a dramatic exit using the same elevator, and the scene cuts while he's still waiting for it to come back up.

Comic Books

There's a sequence in Fantastic Four #2 where Sue turns invisible when government officials come to check on her, then runs out the doorway during their confusion. This act is repeated in the Ultimate Marvel version as well as the movie Rise of the Silver Surfer.
This appears in the Super Mario Adventures comic book. Princess Toadstool fools the Koopalings into coming into her cell with a Ceiling Cling, then beats them up and locks them in.
In Usagi Yojimbo, Tomoe finds herself in trapped in a room in the villain's castle with the guards bound to enter soon. Her solution to pry up some floor boards to make it look like she escaped underneath, and then hide in a nearby trunk until the fooled guards leave the room to continue the search.

Film -- Live Action

In the Peter Sellers movie After The Fox, the titular escape artist and thief pretends to escape, and then succeeds in escaping, by dressing up as the prison doctor, pretending he had been tied up by The Fox, and that the real doctor, who was already out of the building, was in fact The Fox. The Fox is escorted out with much sympathy, and the jailors go chasing after the unfortunate doctor.
- Then, at movies' end, The Fox is back behind bars, and the same situation is played out - but this time the guards 'aren't falling for that again' and leave the doctor tied up in the cell. Outside, The Fox pulls on his disguise beard...and it doesn't come off. He exclaims "My God - the wrong man escaped!"
Goldfinger does this quite well, with James Bond tricking the guard into thinking he's escaped, clinging on to the ceiling, and then dropping down behind him once the guard opens the door.
In Silence of the Lambs, Hannibal Lecter gets bonus points for not even escaping himself, but letting the guards load him into an ambulance, thinking he is their mutilated colleague.

Literature

In Two-Bit Heroes by Doris Egan, the heroine's love interest is going to be displayed in a cage. The outlaw band that she temporarily joined manages to rescue him by building a hidden compartment into the cage beforehand and then causing a distraction while he's on display that makes it look like he's been sorcerously removed, letting him slip into the compartment and get retrieved later.
In The Extraordinary Adventures of Arsène Lupin, Gentleman Burglar, Lupin swears he will escape from jail, and he does, briefly, but gets back in. But when he comes up for trial, Inspector Ganimard suddenly stands up in court and swears that the man in the dock is not Lupin—he has used the fake escape attempt to substitute a flunky in his place. The court has no choice but to let the man go. Of course, the man really was Lupin, and Ganimard fell for it not only because Lupin is a Master of Disguise, but also because he genuinely expected Lupin to fulfill his promise of escaping.
In the Vorkosigan Saga novel Brothers in Arms, Miles gets kidnapped and replaced by a clone. When the clone comes to question him, he considers trying to escape via this trope—claiming that he is the clone and that the real Miles somehow got free and tied him up—but quickly realizes that he has several days' worth of stubble and the clone doesn't, so it's not practical.
In the Illuminatus trilogy, John Dillinger is actually a set of identical quintuplets. This is used to explain how good "he" was at breaking out of prison: if one of "him" was imprisoned, another one could make himself conspicuously visible outside, convincing the guards that he'd escaped and giving the one on the inside more leeway to get out.

Live Action TV

In the Leverage episode "The Jailhouse Job", part of the team's baroque plan to slip Nate out of prison involves using Hardison as a Body Double for another wrongfully-imprisoned prisoner to make it look as though he somehow managed to escape. (Bit of a Casting Gag there—the prisoner was played by Aldis Hodge's Real Life brother.)
In the Stargate Atlantis episode "Aurora", Sheppard finds himself inside a virtual-reality environment simulating a Lantean ship whose inhabitants don't know they're not in the real world. He can enter and exit it at will, but every time he re-enters, he finds himself in the same place he was when he exited. At one point, he escapes from the ship's brig by leaving the environment briefly, waiting for the guard to open the cell to figure out what's going on, and then re-entering it, jumping the guard, and walking out.
In an episode of the french series Les Intrepides (a detective-style show aimed at children), one of the two child protagonists is being held captive in a cabin on a ship. He fashions a makeshift rope out of bedsheets, ties it someplace and tosses it out the window, but it's still too high for him to jump—so he hides. His captors eventually enter the room, see the rope and surmise that he must have jumped anyway. They then leave the door unlocked, allowing him to escape for real.
In The A-Team, Hannibal effects an escape by hiding under his bunk and deceiving his captors into believing he has escaped; they leave the cell door open, and he makes a break for it.
In the "Flight of the War Witch" two part episode of Buck Rogers in the 25th Century, Buck, Princess Ardala and a Pendaran captive use this to get out of their cell. Buck and the captive use a Ceiling Cling to hide, while Princess Ardala simply hides under the bed.
Attempted unsuccessfully in an episode of Sliders, where the titular group slides into a world still stuck in the Old West mode. Quinn and Rembrandt are framed for murder and jailed by the local crime boss and a corrupt sheriff, to be hanged the next day. They realize they could use their knowledge of westerns to trick the guards and escape. Quinn does a Ceiling Cling, while Rembrandt calls for help. Unfortunately for them, the person who walks in is the above-mentioned crime boss, who is also a dimentional traveler (and a Kromagg). He simply walks up to the cell doors without opening them and immediately looks up at Quinn, mentioning that Kromaggs have their own westerns.
In the Mission: Impossible episode "The Crane", the IMF spring a prisoner that is being transported and hide literally metres away from where the escape took place: knowing that the authorities will through a cordon blocks away and gradually work their way inwards.

Video Games

In the third episode of Covert Front, Kara pulls this trope off by leaving her coat on the ground and hiding in a high corner of her jail cell, out of sight. The warden passes by and notices the "empty" cell, and when he goes inside and picks up Kara's coat, she gets the jump on him.
In a way, this is an advanced evasion strategy for the Spy class in Team Fortress 2. Since your cloak takes a half-second to fully activate, and is briefly disrupted when you get shot or touch an enemy, great spies will make it LOOK like you escaped and ran away, in order to get to safety. THEN you actually run away, or attack again. Depending on the situation, pulling this off is the sign of a heavily-experienced spy that you should not take lightly.
One of the ways Snake can escape jail cells he ends up in Metal Gear Solid games is simply hiding under the bed while the guard is gone.

Web Original

As you might expect, the Evil Overlord List has something to say about this.

"I will instruct my guards when checking a cell that appears empty to look for the chamber pot. If the chamber pot is still there, then the prisoner has escaped and they may enter and search for clues. If the chamber pot is not there, then either the prisoner is perched above the lintel waiting to strike them with it or else he decided to take it as a souvenir (in which case he is obviously deeply disturbed and poses no threat). Either way, there's no point in entering."

Western Animation

Done by Jonah Hex in Batman: The Animated Series. There, he is locked in a cell with an earth floor - so he digs a hole, gets into it, and covers himself with his bed. It is unclear what he did with the soil dug out.