If every thing has being then how can non-being, as a concept, not have being?

If every thing has being then how can non-being, as a concept, not have being? Wouldn't it have being by virtue of its distinction from being? I.e. in being 'non-being'- it 'is' that which is 'not being' (the conceptual complement of being) and as it 'is' non-being - distinct from being, it is 'being' no? And so if this is the case, and being is thus a characteristic of all things - then what of being itself?

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