mjhjmtu

Furthermore, take a good person who, going totally beyond the dimension of neither perception nor non-perception, enters and remains in the cessation of perception and feeling. And, having seen with wisdom, their defilements come to an end. This is a mendicant who does not identify with anything, does not identify regarding anything, does not identify through anything.”

https://suttacentral.net/mn113/en/sujato

I don't think the sutta is saying that.

The sutta starts with "What is a good person?", and then, "Is it someone from a good family, an eminent family, a wealthy family? Is a "good" person a famous person?", etc.

And then it gives what I think is standard doctrine, i.e. that it's not because of family's status (e.g. wealth or caste), some "external" factor like that, that a monk is "good" or "better" -- instead it's for what I'd try to call an "internal" reason i.e. it's when "thoughts of greed, hate, or delusion come to an end".

And I think that's it -- that's pretty well the whole sutta. So if you're a monk, don't go thinking you're better than another monk because you came from a wealthy family.

And in fact you shouldn't "identify" like that at all. In English I'd assume that "identifying with" (as that word is used e.g. here) is part of an anatta doctrine, i.e. "Don't start thinking 'I am good because so-and-so is my family' etc." -- and, in Buddhism, also a doctrine about conceit.

Incidentally the word translated as "identifying" is tammaya

absorbed in that; identifying with that; desiring that

So maybe "don't be absorbed with that" or even "don't desire that" could be a translation. I guess I understand from the context, though, why "identifying" makes sense as a translation (or part of the translation) in this context.

To get around to answering your question I guess that nibbana is not only not "identifying" (see also sabbe dhamma anatta as a description of nibbana), perhaps also even not being "absorbed" in (e.g. because it's to do with being "unbound" or "liberated" perhaps).

Also I'm not sure whether "cessation" is an accurate or complete translation in the phrase "cessation of perception and feeling" -- you might want to study how nirodha appears, is used, in the doctrine. The dictionary says " many cases is synonymous with nibbāna", in which case "the nibbana of feeling and cessation" might be a better translation. In which case you'd be asking, "is nibbana the nibbana of feeling and cessation" in which case the answer might more obviously be "yes", whereas the word "cessation" might be misunderstood in this context.

Finally I noticed that at the end of the sutta the word "identify" appears again:

This is a mendicant who does not identify with anything, does not identify regarding anything, does not identify through anything.
Ayaṃ, bhikkhave, bhikkhu na kiñci maññati, na kuhiñci maññati, na kenaci
maññatī”ti.

This time, though, "identify" is a translation of maññati
...

1. to think, to be of opinion, to imagine, to deem ...


2. to know, to be convinced, to be sure ...


3. to imagine, to be proud (of) to be conceited, to boast ...

... instead of atammayatā.

I think that, as explained in Murathan1's answer, nibbana itself doesn't "arise and cease", and that anything conditioned (which does arise and cease, including feelings and perceptions) isn't nibbana.

Even so I don't think that means that attaining nibbana is about being unconscious -- I think that feelings and perceptions continue (to arise and cease), but the arhat doesn't "identify" with them, isn't "absorbed" in them, doesn't "desire" them.

Nibbana

And, having seen with wisdom, their defilements come to an end. This is a mendicant who does not identify with anything, does not identify regarding anything, does not identify through anything.

From the context, I think what Buddha's saying is that, through not identifying with anything, perceptions will no longer cause emotional reactions.

Nibbana is a state that can not be described properly with the words, concepts. That's why Buddhism uses this indirect methodology to describe Nibbana or how to enter Nibbana etc. There is no perception or feeling in Nibbana in the terms of humanly, physical, mental perceptions or feelings. But ultimately Nibbana is beyond physical and mental. It is beyond form. It is the formless, unconditioned, unmanifested, timeless, deathless state. That's why ultimately it is not true to say that there is no perception or feeling in Nibbana. But because it is beyond the form, the perception and feeling in Nibbana can't be described correctly.That's why it is called neither being nor non-being. Also cessation of "perception" and "feeling" (humanly, physical and mental perceptions and feelings) is the way to enter to Nibbana. Nibbana is the birthless, deathless, timeless state. There is no beggining or end for Nibbana.

And when someone's defilements comes to an end, it is impossible to identify with anything again.

Monk Radio: What Happens at Nibbana: https://www.youtube.com/watch?v=83ntwkSWws8

Existence is momentary. One moment is one existence and it arises and it ceases. That doesn't happen in nibbana (that's really the easiest way to understand it). And since life itself is composed totally of those momentary experiences then there really is no such thing as a life that could end: there's only experiences which end every moment. And that doesn't occur, there's no more arising of those momentary experiences: of seeing, hearing, smelling, tasting, and thinking.

What is Nirvana: https://www.youtube.com/watch?v=odWIPhj-ivo