As everyone else has said, we don’t. One of the poster child cases for captive breeding programs is the [black footed ferret](https://en.m.wikipedia.org/wiki/Black-footed_ferret) which was thought to be extinct until a population of 18 was discovered. Now the population is over 1000 in multiple locations to help protect them from complete extinction.
More recently, [the widely thought extinct Vietnamese mouse deer](https://www.cnn.com/2019/11/11/asia/mouse-deer-vietnam-chevrotain-rediscovered-scn/index.html) was captured on game cameras by biologists after having not seen it for 30 years.
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