We don’t, always. And we are occasionally wrong about it. The [coelacanth](https://en.wikipedia.org/wiki/Coelacanth) is a famous example: it was long believed to be a member of a group that had been extinct since the time of the dinosaurs, but turns out to still have some good-sized populations off the coast of southeast Africa (which, at the time, was a very remote place to go study).
But in practice, a species that is still common enough to maintain a breeding population is usually common enough to find if you’re really really looking for it, and extinction usually isn’t declared unless there have been no observations for a while (a decade or more). The only time we know the moment of extinction is if the animal is known to be otherwise extinct but a (usually captive) [endling](https://en.wikipedia.org/wiki/Endling) is known.
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