Fossil species found living off southern California; notes on the genus Cymatioa

They just found a cockroach in Australia that had been thought to be extinct.

So, maybe more common than you'd think? Definitely not common, though - these findings are news for a reason.

I feel like I've seen stories about this sort of thing happening a few times at least; almost invariably the newly [re]discovered animal is very similar to another species that was already known to be alive, so while still a significant discovery it lacks some punch. In this case the presumed-extinct animal is quite similar to C. electilis, which was known to be around in the modern era but apparently is poorly documented (the article says living specimens of C. electilis are undocumented so they could only compare the shells.) These are the only two known living members of the genus and both are rare, so it seems like a fairly significant discovery to me. Not really a case of "animals previously thought to be one species are now reclassified as two", like many other species discoveries seem to be.

I think situations like the Coelacanth, where the rediscovered animal is unlike any other already known to be alive, are quite rare. Although even in that case, the Coelacanth was a revelation to science but probably not the fishermen that caught it.

The linked paper refers to shells in "deposits" dated to between 28,000 and 36,000 years ago rather than fossils, so the species was known to have lived comparatively recently in geologic terms.

A declaration of extinction is a statistical statement - we can’t check under every rock in the world. If we have done a bunch of checking for a species under a bunch of its favorite rocks, and found nothing, the odds are high that it is extinct. But sometimes species beat the odds and a later rock-check finds one after all.