Note one.
All dialogues with deniers of the idea of complete cessation actually rest on one single topic.
Did Buddha consider the five aggregates & six spheres of contact, etc.
a) as a holistic, all-encompassing description of experience, including “All”, or
b) as an exclusive, limited one, in which the lower, contaminated, gross, dualistic, conceptual forms of experience, mind and matter are described.
It is reasonable to assume that in his categorizations the Buddha described everything that is, All experience. This is indicated by the very term “aggregate”, as a kind of heap or all-encompassing collection of anything. Or the name of the six spheres of contact as “All”, beyond which anything else cannot be known, since knowledge is included in “All”, or as “World”, hinting at the all-encompassing character of these categorizations of experience, extending to the concepts of the universe, the world, everything that is.
Therefore, if the aggregates & spheres of contact are considered dukkha, then their cessation is nibbana and this means the complete cessation of everything, beyond which there is no speculation of some residual other entities. And the topic is closed immediately.
Note two.
Buddha looks at a being and analyzes it into some aspects of mind and matter. Then he asks a question.
‘Is this permanent or not permanent?’ - impermanent.
‘And is that which is impermanent suffering or pleasant?’ - suffering.
‘And is that which is impermanent, suffering, subject to change, reasonable to consider as one’s atta?’ - no, it is not reasonable.
And so, if we see any experience or awareness of something, any ‘reality’, which does not seem to be included in the five aggregates & six spheres of contact, then we must ask ourselves: is this impermanent and conditioned?
If yes, then it is Dukkha.
And Dukkha in Nibbana ceases without remainder.
But if it is not impermanent and unconditioned, then it is happiness, pleasant. And it is reasonable to call it one’s atta.
Such is the logic of the denial of atta. And applying this logic we get Atta in the case of a permanent and unconditioned experience or awareness. But there is no Atta in Nibbana! It is empty of Atta.
So in Nibbana there is neither dukkha nor atta. It is empty of both. Of the impermanent, conditioned minds and of the hypothetical permanent, unconditioned minds. What is the permanent unconditioned mind but the jivatma, the soul - that is, the spiritual essence, the part of the personality that lasts for eternity? And the force with which people cling to the idea of a soul in any form shows why the Buddha chose to deny precisely this idea in his teaching on anatta and sunyata.