In AN10.7 Venerable Sāriputta says he was meditating in such a way he wasn’t even perceiving the state of neither-awareness-nor-nonawareness (or ‘neither-perception-nor-nonperception’), yet at the same time he was still aware. This is paradoxical, because beyond this state of meditation there is only the cessation of all awareness, so how could Sāriputta still be aware? The answer lies in his subject of meditation. The perception he was cultivating was, “the cessation of existence is extinguishment” (bhavanirodho nibbānaṃ).
This perception entails the realization that the cessation of existence is indeed the goal of the Buddha’s path, as well as perceiving it to have the positive qualities of peace and coolness associated with the term ‘extinguishment’. It is a cognitive understanding of what the goal is, not a direct experience of it. (Compare Schmithausen, On Some Aspects of Descriptions or Theories of Liberating Insight and Enlightenment in Early Buddhism, p.227–228; contra Anālayo, The Signless and the Deathless, Chapter II.3.)
In the preceding discourse (AN10.6), Sāriputta also says he was cultivating a perception that paradoxically went beyond perception, reflecting that extinguishment is peaceful and sublime. This too is a contemplation of certain qualities of extinguishment, which is further clarified when in AN10.60 the same perception is explicitly described and as a reflection/consideration (paṭisañcikkhati), alongside such reflections that the aggregates are impermanent and that the body is liable to sickness. It is also described as a thought in AN3.32. The reflection “the cessation of existence is extinguishment” in SN12.68 is called “personal knowledge” (paccattaṃ ñāṇaṁ). It is described in the exact same way as the personal knowledge that death depends on birth—followed by the other links of Dependent Arising—which likewise is not a direct experience of birth or death but a cognitive understanding of their relationship. (However, while the connection between birth and death is to some extent obvious to all, the knowledge of extinguishment is based on profound and direct insight into cessation.) The commentary also calls the perception a ‘reviewing/reflection’ (paccavekkhaṇā).
In the latter discourse “the cessation of existence is extinguishment” is the knowledge of an enlightened being but also that of a trainee (sekha), so this perception is available to all noble ones, including the stream winners. Stream winners directly realized that their existence is going to cease after a few more lives at most. For them, the perception on extinguishment is a recollection of this realization, which will incline their mind further towards letting go of suffering. For enlightened beings the perception will be based on their knowledge that existence is going to cease at the end of this life. It is a reflection on their knowledge that “there won’t be a next existence” (e.g. SN35.72, Thag1.67). In MN49 the Buddha himself says he knows existence will come to an end, specifically using a future verb form. For fully enlightened ones like him, this is just a known fact which serves no further purpose to develop the mind. (In some other places enlightened ones say, “all states of existence are ended”, e.g. Thig 5.5, but with bhava in the plural, this refers to future lives, to having ended rebirth in all realms.)
That the reflection on the cessation of existence concerns the extinguishment that happens at an enlightened being’s death, can also be derived from Iti44, which says all existence only ceases after this life (samparāyikā), at the kind of extinguishment which leaves no remnant (anupādisesā nibbānadhātu), also known colloquially as full extinguishment (parinibbāna). Sāriputta obviously hadn’t reached this yet, but he was reflecting on it, knowing that it was going to happen. (Contra Ñāṇananda, The Magic of the Mind, p72–75, who states: “This experience of the cessation of existence (bhavanirodho), which is none other than ‘Nibbāna here-and-now’.”)
Sāriputta’s point is, since this perception is a reflection on the cessation of existence including all awareness, it in a sense goes beyond the state of neither-awareness-nor-nonawareness, where there still is a tiny bit of awareness left. However, it still is a reflective perception, not the actual cessation of awareness itself, so in that sense it doesn’t go beyond it.
The paradox therefore simply revolves around what we mean by ‘percipient of’ and ‘going beyond’. It is not the case that the nature of extinguishment is inherently paradoxical, that there exists a unique type of perception that isn’t a perception. The Pāli word saññā, just like the English ‘perception’, can both mean a cognitive understanding of something or mere awareness of something. (See also Hamilton, Identity and Experience, p.62: “Throughout the Sutta the word saññā is used in the sense of ‘consciousness’ […] but it is also used in the sense of the arising or cessation of particular ‘conceptions’ […] achieved through training the mind […]”.) Sāriputta was cultivating a perception, in the sense of a cognitive understanding, of the cessation of perception, in the sense of awareness.
In other words, when reflecting on extinguishment it is not really proper to say you are still percipient of anything constructed, yet at the same time it is still a constructed perception.