If you say "The existing possibility that existence and nonexistence exist necessarily exists" and define "necessary" as "Absolutely must exist", there can be no nonexistence, because you implicitly (and correctly) posit Existence beyond existence and nonexistence. So, talking about nonexistence is moot. Or better said, you don't talk about absolutes, but merely its forms or their lack (and so your vocabulary is at this point more than misleading).