Since nobody else mentioned it (for any given reason), I might as well take a shot: what about "nothingness"? At first, it would sound as a silly answer, but it deserves some thought.

The concept of sheer nothingness can make itself quite clear, as the utter absence of any element admitted into existence (be it fantasy-related, idealistic or abstract). And (quite obviously) nothingness continues to unexist whether we mention its name or not. The point is: while we are in the process or uttering this word, it exists. But as soon as we finish, the result leads to nothingness once more, as it is addressed to the concept of non-existence. I found it worthy of some meditation.

Lastly, I'll avoid getting into philosophical manners about existence or the opposite, since it would not only be a waste of time, but wouldn't also contribute to the solution of such an interesting riddle. Aside all that, the "silence" answer seems to fit nicely as well.