Breeds can indeed become extinct.
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I just can't see it that way, a very popular dog at one time was the half German Shepherd, half Collie cross, I don't know if people still breed them but anyone who has German Shepherds and Collies can easily produce them tomorrow, at the same time the German Shepherd and the Collie are just products of selective breeding, as long as there are dogs all these varieties can be produced by selective breeding. A truly extinct animal cannot be brought back in this way.
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.