We can talk about things before and after they "exist". For example, a pencil did not always exist, but was previously a tree, and after it is used it is a pile of wood scraps. Probably most of us would say the pencil "exists" when we are able to use it as a pencil - it has a graphite point, you can hold and write with it, etc.

But is it correct to say that the pencil did not previously "exist" before we see it as this tangible, material object? In my opinion it seems as though this pencil actually did exist before it "exists" - in the mode of being a possibility, or a concept, or an idea (before), or as a memory, footprint, etc (after).

We have a habit of identifying things that exist when they are present-at-hand - they seem to exist in a finite spatial-temporal location. But if this is truly what "existence" means, then it seems hard to explain how we can talk meaningfully about things that do not exist.

But I think we actually can talk about things that don't exist - but only because they actually do exist, just not in a material, tangible, extended way. A pencil does not simply exist when it is actually extended in space-time, for that is only a "mode" or "way" of existing. It can also exist as a possibility, a guarantee, a contradiction, a memory. To say "the pencil does not exist" cannot mean that the pencil literally does not exist, for obviously we are talking about the pencil and therefore the pencil exists in some other way, as an idea or a concept or what have you.

The rub is that it is impossible to talk about something that does not "exist" without therefore bringing it into existence, or at least recognizing that this thing exists in some form. Therefore when we say things like "the dinosaurs no longer exist", what we really mean is that "the dinosaurs no longer exist in any material, tangible, extended way." - but they do still exist as a memory. When the dinosaurs existed in this material way, they were not a memory. The coming-in-and-out of existence is really simply a change of mode of existence, to and from one that is more or less causally relevant.