When we classify an animal as being extinct, what chances exist for it to still exist in remote areas and do guidelines for classifying something as extinct account for this possibility?

I was considering how during many times during my wilderness hikes I come across strange insects, and it made me consider a broader thought about whether or not any of these insects were “rare”…

This led me to considering how someone in any remote locale and without the “know” could very well see something considered by scientists to be “extinct” but such and such person never knowing it’s “extinct”.

This led me to then wondering what the chances are that some extinct creatures might not be extinct at all, just removed from the people who would be observing it and looking for it, and perhaps accounting for it.

Because of this, I was sort of wondering what the “policy” is for declaring something as “extinct”, given the massive size of the world and the variables given of even people coming across these animals commonly, not knowing they are extinct or even rare, and not even having knowledge about communicating the rarity or extinction to the correct sources, because they wouldn’t even know of such a thing about the animals and “extinction” to begin with

I know I’ve offered a word salad, but I hope I’m making some sense.

Thanks!