Caught in a storm or Negative Space Wedgie, one or a party of travellers happen on a long-lost scientist or wizard (depending on the setting). This person has considerable local power, often with some kind of slaves or robots to do his bidding, but either cannot leave their place of exile, or chooses not to.
This is a trope about accidental rediscovery (at least from the traveller's point of view). If the travellers have gone looking for the lost scientist or wizard then they are more likely to be seeking a Hermit Guru.
In most cases the Affably Evil lost scientist or wizard has either a dark secret or a sinister goal that requires the travellers. He may have a supporting cast of servants or slaves, and may also have a beautiful daughter to provide romantic interest, typically introduced in a No, Mr. Bond, I Expect You to Dine scene. He may be famously lost so that one of the heroes can fill in his Back Story by starting with "I read about him at school...". Any unusual equipment that he has is justified by A Wizard Did It.
If the lost scientist or wizard is not evil then he may have been secretly watching the party and decided that these people are worthy of help, usually some form of Applied Phlebotinum. The arrival of the right heroes can also induce a HeelFace Turn on the part of an evil scientist/wizard, or induce a formerly good one to take off their Jade-Colored Glasses.
The earliest known version of this trope is The Tempest (making it Older Than Steam), in which the exiled wizard Prospero causes a storm in order to bring a party travelling by sea onto his island in order to wreak revenge. The setting of a lost wizard on an island won't work in the modern world, but the concept has been Recycled In Space several times, most famously in Forbidden Planet, with a scientist on a planet instead of a wizard on an island. The lost scientists in these versions lack Prospero's Invisibility Cloak, so only the dark secret or motive is kept hidden. Instead the relationship between the travellers and the scientist is used to drive a mystery plot with the travellers gradually realizing that all is not as it seems.
- Forbidden Planet is The Tempest IN SPACE!, with Prospero replaced by Dr. Edward Morbius.
- The Black Hole had the lost scientist Dr. Reinhardt alone on a giant ship full of robots some of who turn out to be the original crew with mind-control implants, plus big robot Maximillian as The Dragon. The eponymous black hole is the Negative Space Wedgie.
- A New Hope has Luke 'accidentally' meet Obi-Wan Kenobi, samurai space-wizard. Later it transpires that Kenobi has been keeping a close eye on Luke, and their meeting was no accident.
- BIONICLE: in "Riddle of the Great Beings", Tarduk and his group, on their their journey to Northern Bara Magna, encounter Surel, a warrior thought lost from the Core War.
- The Mysterious Island by Jules Verne is a sequel to 20,000 Leagues Under The Sea in which five American balloonists are marooned on an island in the South Pacific. They eventually discover the aged Captain Nemo still living in the Nautilus, which is hidden in a cave under the island. Nemo turns out to have been behind a number of strange but helpful events in the story
- In The Island of Doctor Moreau by H.G. Wells, the protagonist discovers Dr Moreau, formerly an eminent physiologist in London, experimenting with the uplift of animals to humans through painful surgery.
- In the World of Warcraft novel Cycle of Hatred, Jaina Proudmoore is looking for a place to create a settlement and stumbles on a hidden shack protected by powerful wards. After bypassing the wards, she discovers Aegwynn, the only female Guardian of Tirisfal and Jaina's childhood hero. Aegwynn ends up helping Jaina defeat a demon and becomes her secret advisor.
- In Everworld, Merlin follows the characters around, trying to capture Senna; and when he is encountered, it is often this trope. He means no harm to the characters other than Senna; and even with Senna, he wishes she would understand that his attempts to capture her are for the greater good of both Everworld and Senna's own safety (she doesn't ever see it this way).
- In Hour of the Dragon, an unconscious Conan the Barbarian is found and healed by a hermit witch. When he tells her what's happening to Cimmeria, she decides to help fight for the country's freedom.
- Star Trek: The Original Series used this a couple of times:
- "Metamorphosis": Lost scientist Zefram Cochrane, inventor of the warp drive, is discovered by the Enterprise.
- "Requiem For Methuselah": Mr. Flint owns a planet in the Omega system. He has a number of robots as servants and a beautiful female ward named Rayna Kapec. He has tremendous technological power, enough to destroy the Enterprise. He has two dark secrets. The first is that he is an immortal man from Earth and is thousands of years old. The second is that his ward is not human, but actually an android robot in female form, and he needs to have her emotions wakened so she will love him. Her name may be a reference to Karel Čapek, who coined the word "robot".
- Babylon 5: Sheridan meeting Lorien on Z'ha'dum. Lorien had been living there for millennia, and as he was the First One, the Shadows had built their stronghold around this place out of a largely-forgotten veneration. Sheridan was the first of the young races to "come this far" and actually meet Lorien, who then became instrumental in helping him. Since he has some powers that might be described as "supernatural", one could say he's a "lost wizard" of sorts. Lorien has no sinister motive, but that doesn't stop Garibaldi suspecting him of one.
- The Tempest. Wizard Prospero is the exiled Duke of Milan with Ariel and Caliban as his slaves and Miranda as the daughter. Prospero starts out intending to revenge himself on the shipwrecked party, but changes his mind after Miranda falls in love with one of them.
- Charles Ludlam's play Utopia, Incorporated borrows liberally from the plot of The Tempest, and thus has Anarch, leader of the utopian island (with beautiful daughter).
- Knights of the Old Republic: The party is sent down to the Kashyyyk Shadowlands. They soon stumble on Jolee Bindo, a self-exiled Jedi who is aware that he's known as "the crazy old man in the dangerous woods," and volunteers himself into the party in exchange for leading them to the Plot Coupon. And yes, he knew exactly who the Player Character was (or is), but figured it wasn't his place to say anything. Jolee is nothing if not very meta about the whole concept.
- Up by Pixar has the explorer Charles F. Muntz with a huge pack of talking dogs living in his airship. In the No, Mr. Bond, I Expect You to Dine scene the cook is one of his dogs.
- Played for Laughs in Shrek the Third. Merlin is portrayed as a mentally unstable teacher who was forced to leave the school where he taught.
- On Surf's Up, after Cody gets hurt surfing, lifeguard Nani takes her to her uncle Zeke, a reclusive hermit living in the jungle, to recuperate. Eventually, Cody recognizes Zeke for who he really is - his childhood surfing idol Big Z, who faked his own death to get away from the limelight.