Not So Extinct

"Dinosaurs are extinct, so you never can tell where you'll find them."

—Hadji in "The Sea Haunt", Jonny Quest

Everyone knows that dragons (or elves, or fairies, or Prehistoric Monsters, or whatever race it may be) have been extinct for thousands of years...but if they're all gone, why is this story taking such pains to mention them? It's a safe bet that they aren't extinct at all, and that you'll meet one by the end of the story (if not sooner).

Also applies if the creature in question is thought to be a myth. A form of Chekhov's Gun. May involve an Egg McGuffin.

This is generally a fantasy trope. If it happens in the real world, or if the story revolves around an extinct creature being discovered, it's Species Lost and Found.

Examples of Not So Extinct include:

Anime

In Negima Second Season, Asuna spends 24 out of 26 episodes looking the Chupacabra which everyone says doesn't exist; they create a Chupacabra school club and order T-shirts and other items. At the end of the series, she finds one (which she quickly puts to work signing T-shirts.)

Literature

Downplayed in Harry Potter. Word of God states that while none of the creatures Luna "Looney" Lovegood claims exist actually exist, the fact that she accepts their existence helped her in discovering many real magical creatures that were previously unknown.
In The Hollows, it's widely believed that elves were wiped out in the Turn, but a few survived, including Trent, Jonathan, and Quen.
On the Discworld a lot of standard fantasy creatures are extinct, though that's often synonymous with "trapped in a parallel dimension."
- Giant, flying, fire-breathing dragons are shunted off in a dimension of their own. Their improbable biology requires magic to sustain, and the Discworld generally doesn't have enough magical energy around for them to exist anymore. There are exceptions, small pockets of high magic where dragons survive, and individual dragons can be summoned if enough magical energy is pumped into them.
- Elves are similarly stuck in their own dimension(s), although there are weak points where travel is possible - lots of them in the Ramtop mountains.
- Orks were the foot soldiers of the defunct Evil Empire, and it's revealed in Unseen Academicals that the people of Uberwald have been exterminating the few survivors. They haven't been entirely successful.
Animorphs does this with the Venber in "The Extreme". Though they're actually hybrids of Venber and humans brought back by the Yeerks.

Live Action TV

Game of Thrones has two explicit examples of creatures widely believed to be extinct at the start. People are... less sure by the end of the season.
Supernatural: The attack pattern of the Monster of the Week points to a dragon, but dragons are extinct...except this one.