Does nibbana exist?

From the Visuddhimagga Part III, Ch XVI:

“[DISCUSSION ON NIBBÁNA]

  1. [Question 1] Is Nibbána non-existent because it is unapprehendable, like
    the hare’s horn?

[Answer] That is not so, because it is apprehendable by the [right] means. For
it is apprehendable [by some, namely, the nobles ones] by the [right] means, in
other words, by the way that is appropriate to it, [the way of virtue, concentration,
and understanding]; it is like the supramundane consciousness of others, [which
is apprehendable only by certain of the Noble Ones] by means of knowledge of
penetration of others’ minds. Therefore it should not be said that it is non-existent
because unapprehendable; for it should not be said that what the foolish ordinary
man does not apprehend is unapprehendable.

  1. Again, it should not be said that Nibbána does not exist. Why not? Because
    it then follows that the way would be futile. [508] For if Nibbána were nonexistent,
    then it would follow that the right way, which includes the three
    aggregates beginning with virtue and is headed by right understanding, would
    be futile. And it is not futile because it does reach Nibbána.”

The problem is some people looking at words like rāgakkhayo dosakkhayo mohakkhayo etc, convert this to English and ask how can a cessation exist.

It is on coming to Nibbana(nibbānaṃ āgamma) depending on Nibbana(nibbānaṃ paṭicca) they cease. Hence, phalūpacāra vasena they are all terms for Nibbana.

The closest English equivalent might be
Agent-Centered Functional Naming.

‘Cure’ is what cures (the sickness)

‘Solution’ is what solves (the problem)

Coming to Nibbana how? In terms of taking as object.

Objects are causes as well, for example paracitta to paracitta vijānana ñāṇa.

yāvatā, bhikkhave, dhammā saṅkhatā vā asaṅkhatā vā, virāgo tesaṃ aggamakkhāyati, yadidaṃ madanimmadano pipāsavinayo ālayasamugghāto vaṭṭupacchedo taṇhakkhayo virāgo nirodho nibbānaṃ.
~Iti90

Reflection on Nibbana is one of the 40 subjects of meditation. In AN 11.12 & 13, the Buddha advises a layperson and lists the results of recollections, which include “a sense of the goal,” meaning nibbana is a recommended reflection from the earliest stages.