People with Cotard's syndrome, for instance, can think that they don't exist, an impossibility for Descartes. Broks describes it as a kind of "nihilistic delusion" in which they "have no sense of being alive in the moment, but they'll give you their life history". They think, but they do not have sense that therefore they are.
Then there is temporal lobe epilepsy, which can give sufferers an experience called transient epileptic amnesia. "The world around them stays just as real and vivid – in fact, even more vivid sometimes – but they have no sense of who they are," Broks explains. This reminds me of Georg Lichtenberg's correction of Descartes, who he claims was entitled to deduce from "I think" only the conclusion that "there is thought". This is precisely how it can seem to people with temporal lobe epilepsy: there is thought, but they have no idea whose thought it is.
You don't need to have a serious neural pathology to experience the separation of sense of self and conscious experience. Millions of people have claimed to get this feeling from meditation, and many thousands more from ingesting certain drugs.
In the days of classical Greece, the Solopsists were a school of philosophers who wondered whether you were all there was in existence--everything else was in your imagination. After all, how can you prove that anything, much less anybody, exists? But this is very different from somehow feeling that even you yourself don't exist, and that is hard to imagine to those of us who, well, know that we do. Or at least think we do!
In the 18th Century, Immanuel Kant discussed the problem of our knowing only what our sensory systems tell us, rather than what things actually are in themselves. He assumed that those things existed, but dealt with the consequences of our limited ability to know them directly. But again, at least the issue is what we know about what's 'out there' rather than what's 'in here'.
In modern times, there were many noteworthy attempts to grapple with the former issue. But what is 'self'? Whether we state it thus or not, it usually boils down to consciousness. And there is of course the view that only us perfect humans have it. That is very un-evolutionary thinking, since nothing so complex arises out of nothing.
Research into consciousness faces many barriers, not least of which is that it is presently impossible to objectively study something that is entirely (indeed, by definition) subjective. Going back to the founder of modern psychology, William James, to the present--including the last years of work by Francis Crick (discoverer of DNA structure)--what we do is to study what we can see or measure about the study subject. These have recently been referred to as the 'neural correlates of consciousness'.
We can ask people what they experience, but we can't ask a functioning brain that does not have conscious responsiveness how it feels about itself. But, from the kinds of work that have been done, it seems unlikely that people whose brains have been damaged, yet who can respond to the world but do not have 'consciousness' (including the 'split-brain' subjects, whose hemispheres have been surgically separated to treat severe epilepsy)--it seems unlikely they can tell us that they do not exist.
As a result, whatever this story is actually reporting, probably no reader of this post can directly report experiencing non-existence, so we can only think about what those who say they do have that experience could possibly mean. Or consider the carrot: it's a complex, organized living structure, presumably without consciousness....but does it have self-awareness?
Neuroscience and psychology provide plenty of data to support the view that common sense is wrong when it thinks that the "I" is a separate entity from the thoughts and experiences it has. But it does not therefore show that this "I" is just an illusion. There is what I call an Ego Trick, but it is not that the self doesn't exist, only that it is not what we generally assume it to be.This is a mind-bender, a philosophical as much as scientific, phenomenon. Are you you....or aren't you?