Extinct in the Wild
A species that is extinct in the wild (EW) is one that has been categorized by the International Union for Conservation of Nature as only consisting of living members kept in captivity or as a naturalized population outside its historic range. Classification requires exhaustive surveys conducted within the species' known habitat with consideration given to seasonality, time of day, and life cycle. Once a species is classified as EW, the only way for it to be downgraded is through reintroduction.
Not all EW species are rare. An example is the Brugmansia family, where all seven species are widely cultivated, but none are found in the wild. Ultimately, the purpose of preserving biodiversity is to maintain ecological function to prevent ecological extinction.
Reference: wikipedia