The California Spangled is extinct but, that said, cat breeds can’t become extinct.
Sarah Hartwell says, “The breed was considered extinct in the 1990s”. You won’t get a better authority. This is about 20 years ago. If there were some individual cats with some breeders perhaps they have died. There may be some individual cats left but very few. The breed did not gain traction to use a modern phrase. It did not progress beyond ‘new breed or color’ at TICA or ACA, two cat associations.
The failure of the California Spangled to become successful like the Bengal cat is probably down to bad luck and perhaps the domination of the true wild cat hybrids with which the American cat loving public became fascinated. The California Spangled is not a wild cat hybrid but a creation through selective breeding of domestic cats. You can read about the history in detail on this page (the best page on the internet about the creation of this breed). A modern equivalent of the Calif. Spangled is the Ocicat which itself is not that popular – drowned out by the Bengal.
Which brings me to the question in the title, can a cat breed become extinct? I don’t believe they can. A lot of cat breeds such as the California Spangled are created by people. Therefore they can be recreated. Although I say ‘recreated’ the result would possibly be somewhat different. Extinction only applies to nature. The word refers to species of animals rather than a ‘breed’. Breeds are not species. All cat breeds are one species; the domestic cat felis silvestris catus.
A wild cat such as the Asian leopard cat can (the wild ancestor of the Bengal) can become extinct. We know that. But a lot of well-known cat breeds such as the Persian and Ragdoll are modern creations. Although the Persian cat is one of the originals going back to the mid-to-late 1800s, it has been constantly selectively bred and altered such that I have called it a modern creation.
Breeders could start again if they had to. In fact, it could be argued that some breeds would be improved if they were restarted because it would improve their health with a wider gene pool. Also the Persian has no connection with the ‘original’ (if there is such a cat) and a restart of that breed could improve it by making it more purebred and truer to the original. It might also rekindle interest in the established breeds if they were ‘restarted’.
Technically, a wild cat hybrid such as the Bengal could become extinct if the leopard cat become extinct as well the breed.