Just a short general comment on this topic. I’ve mostly just laid aside this whole fourfold negation question with respect to the status of an arahant. At this point, it just seems too mysterious and confusing to me.
That said, I don’t find the explanation sometimes given that the Tathagatha doesn’t really exist before death and therefore the question of their status is inapplicable after death also, entirely satisfactory. Firstly, ruling out the four cases: exists/not exists/both exists and not exists/neither exists nor not exists, is, as far as I can recollect, only ever applied in the suttas to an arahant or the Tathagatha himself. It’s not applied to earlier path stages or ordinary followers, i.e., there are no statements such as you don’t really exist now and therefore existence isn’t really applicable in the future either. Secondly, it is clear that this four case inapplicability is valid for the living arahant or Tathagatha. This is consistent with statements in various places about the untraceability of such beings even in this life.
I think that whatever this fourfold inapplicability/negation is referring to likely is special and particular and holds only for beings after full enlightenment (something has fundamentally changed when alive, which leads on to this inapplicability after death, and this untraceability when living).
As it says in the Khema sutta:
“No, ma’am. Why is that? Because the ocean is deep, immeasurable, and hard to fathom.”
“In the same way, great king, any form by which a Realized One might be described has been cut off at the root, made like a palm stump, obliterated, and unable to arise in the future. A Realized One is freed from reckoning in terms of form. They’re deep, immeasurable, and hard to fathom, like the ocean. To say that after death, a Realized One exists, or doesn’t exist, or both exists and doesn’t exist, or neither exists nor doesn’t exist: none of these apply.
Any feeling … perception … choices … consciousness by which a Realized One might be described has been cut off at the root, made like a palm stump, obliterated, and unable to arise in the future. A Realized One is freed from reckoning in terms of consciousness. They’re deep, immeasurable, and hard to fathom, like the ocean. To say that after death, a Realized One exists, or doesn’t exist, or both exists and doesn’t exist, or neither exists nor doesn’t exist: none of these apply.”