Some extinct breeds can be re-constituted, some can't. For example, the Smithfield collie became extinct and stayed that way because nobody knows how to re-constitute it. Some believe that the Rottweiler is the re-constitution of the ancient Roman camp dog, but nobody knows for sure. Same story for the British drover's cur.
Breeds can and do become extinct. Some are brought back, some aren't.
In biology and ecology, extinction is the cessation of existence of a species or group of taxa, reducing biodiversity. The moment of extinction is generally considered to be the death of the last individual of that species
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