If inexistence exists then how is it inexistence? And if inexistence does not exist then how come it into existence and we know about it? Or is it paradox?
Already the question about the existence of existence is based on a delicate linguistic expression:
Primarily single objects exist. Everybody understands a sentence like: There exist people from Norway. But already the question, whether abstract concepts exist, and if yes, in which sense they exist, is debated. E.g., in which sense exist "humanity" or in which sense exist mathematical objects?
I consider existence and non-existence an abstract concept, namely a property of possible objects. Then one can deal with the question of the existence of these two properties in alike fashion.
Of course this approach does not answer the original question. But as stated above, the question has no generally accepted answer. For more information cf. the philosophical terms nominalism versus realism.