OUCH, that is a harsh way of putting it. God's existence would be in non-existence.
I suppose an example near at hand for what you mean would be intelligence. The problem that this is runs into is that intelligence derives its stuff from existing things. As Hume knew, existence cannot be deduced from essence. It must be the other way around. Indeed existing things are the content determinig causes of our thinking and knowing. As Gilson writes, "All real knowledges is by nature both essential and existential. Being does not come first in the sense that what comes next no longer is being. Being comes first and it stays there."
Gilson continues it a fine description of participation:
To know a thing is to be it in an intellectual way. The classical refutation of adequatio rei et intellectus which the concept is supposed to be a passive reflection of reality, entirely misses the point. It may well apply to naive essentialism, but it by no means applies to a noetic in which the knowledge of essence rests upon the vital conjunction of two acts of existing. Even abstract knowledge is not the mere copying of an essence by an intellect; it is the intellectual becoming of an actual essence in an intellectual being.
Wouldn't the distinction "possible" and "actual" be sufficient? The terms of negation work too quick to efface the participatory nature of all things.
That's certainly true; and the words "possible" and "actual" might be good substitutes. But the term "non-existent reality" -- which I'm sure you're aware is Voegelin's and Sandoz's -- is proposed in order to draw a distinction between what is accessible to direct sense perception ("existent" i.e. physical reality) and what is not ("non-existent" reality), the latter being accessible to apperception (or noesis). It has a limited usefulness in that sense.
I really liked this, from Gilson:
Even abstract knowledge is not the mere copying of an essence by an intellect; it is the intellectual becoming of an actual essence in an intellectual being.In short, via a noetic experience -- the sort of thing that belongs to "non-existent reality," in Voegelin's sense.
Thank you so much for writing, cornelis!