Is it possible that members of known extinct clades are hiding somewhere? For example is it possible that trilobites could be found in deep sea trenches, primitive mammals or premammalian synapsids, small mecosuchins, other sphenodonts, madtsoiid snakes, and others could be found deep in Australia and New Guinea, and multituberculates deep in China? The discovery of the very tall Wolllemi pine just in 1994 in Australia and some peculiar invertebrates Dendrogramma near Australia in the 80s gives us some hope. Why no one has funded a program for search of potential living fossils?

Some of these are probably possible. The difficulty with, for example, trilobites is that they're not merely unknown in present ecosystems, but unknown from fossils more recent than the end-Permian mass extinction 250 million years ago. So for trilobites to have survived, they'd need to have done so in a way that obscured a quarter of a billion years' worth of fossils. I won't say it's impossible -- perhaps they live only in very deep parts of the ocean which never come to the surface where the fossils can be seen. But it seems unlikely.

Why no one has funded a program for search of potential living fossils? Well, how would you do that? Where would you look? How could your search be focussed on living fossils only? I think that any natural history field expedition would be delighted to find specimens like these if they turned up, but that's just as likely to happen while they're working on something more tractable than if they're wandering at random in the hope of spotting relict taxa.