The following is the Buddha's response to just such a question, put to him by the wanderer Vacchagotta, in the Aggi-Vacchagotta Sutta (MN 72):
"Does Master Gotama have any position at all?"
"A 'position,' Vaccha, is something that a Tathagata has done away with. What a Tathagata sees is this: 'Such is form, such its origin, such its disappearance; such is feeling, such its origin, such its disappearance; such is perception... such are mental fabrications... such is consciousness, such its origin, such its disappearance.' Because of this, I say, a Tathagata -- with the ending, fading out, cessation, renunciation, & relinquishment of all construings, all excogitations, all I-making & mine-making & obsession with conceit -- is, through lack of clinging/sustenance, released."
"But, Master Gotama, the monk whose mind is thus released: Where does he reappear?"
"'Reappear,' Vaccha, doesn't apply."
"In that case, Master Gotama, he does not reappear?"
"'Does not reappear,' Vaccha, doesn't apply."
"...both does & does not reappear?"
"...doesn't apply."
"...neither does nor does not reappear?"
"...doesn't apply."
"How is it, Master Gotama, when Master Gotama is asked if the monk reappears... does not reappear... both does & does not reappear... neither does nor does not reappear, he says, '...doesn't apply' in each case. At this point, Master Gotama, I am befuddled; at this point, confused. The modicum of clarity coming to me from your earlier conversation is now obscured."
"Of course you're befuddled, Vaccha. Of course you're confused. Deep, Vaccha, is this phenomenon, hard to see, hard to realize, tranquil, refined, beyond the scope of conjecture, subtle, to-be-experienced by the wise. For those with other views, other practices, other satisfactions, other aims, other teachers, it is difficult to know. That being the case, I will now put some questions to you. Answer as you see fit. What do you think, Vaccha: If a fire were burning in front of you, would you know that, 'This fire is burning in front of me'?"
"...yes..."
"And suppose someone were to ask you, Vaccha, 'This fire burning in front of you, dependent on what is it burning?' Thus asked, how would you reply?"
"...I would reply, 'This fire burning in front of me is burning dependent on grass & timber as its sustenance.'"
"If the fire burning in front of you were to go out, would you know that, 'This fire burning in front of me has gone out'?"
"...yes..."
"And suppose someone were to ask you, 'This fire that has gone out in front of you, in which direction from here has it gone? East? West? North? Or south?' Thus asked, how would you reply?"
"That doesn't apply, Master Gotama. Any fire burning dependent on a sustenance of grass and timber, being unnourished -- from having consumed that sustenance and not being offered any other -- is classified simply as 'out' (unbound)."
"Even so, Vaccha, any physical form by which one describing the Tathagata would describe him: That the Tathagata has abandoned, its root destroyed, like an uprooted palm tree, deprived of the conditions of existence, not destined for future arising. Freed from the classification of form, Vaccha, the Tathagata is deep, boundless, hard to fathom, like the sea. 'Reappears' doesn't apply. 'Does not reappear' doesn't apply. 'Both does & does not reappear' doesn't apply. 'Neither reappears nor does not reappear' doesn't apply.
"Any feeling... Any perception... Any mental fabrication...
"Any consciousness by which one describing the Tathagata would describe him: That the Tathagata has abandoned, its root destroyed, like an uprooted palm tree, deprived of the conditions of existence, not destined for future arising. Freed from the classification of consciousness, Vaccha, the Tathagata is deep, boundless, hard to fathom, like the sea. 'Reappears' doesn't apply. 'Does not reappear' doesn't apply. 'Both does & does not reappear' doesn't apply. 'Neither reappears nor does not reappear' doesn't apply."
When this was said, the wanderer Vacchagotta said to the Blessed One: "Master Gotama, it is as if there were a great sala tree not far from a village or town: From inconstancy, its branches and leaves would wear away, its bark would wear away, its sapwood would wear away, so that on a later occasion -- divested of branches, leaves, bark, & sapwood -- it would stand as pure heartwood. In the same way, Master Gotama's words are divested of branches, leaves, bark, & sapwood and stand as pure heartwood.
"Magnificent, Master Gotama! Magnificent! Just as if he were to place upright what was overturned, to reveal what was hidden, to show the way to one who was lost, or were to carry a lamp into the dark so that those with eyes could see forms, in the same way has Master Gotama has -- through many lines of reasoning -- made the Dhamma clear. I go to Master Gotama for refuge, to the Dhamma, and to the Sangha of monks. May Master Gotama remember me as a lay follower who has gone to him for refuge, from this day forward, for life."
And elsewhere, in Sn 5.6: Upasiva-manava-puccha, the following exchange is recorded:
Upasiva: He who has reached the end:
Does he not exist, or is he for eternity free from dis-ease?
Please, sage, declare this to me
as this phenomenon (dhamma) has been known by you.
The Buddha: One who has reached the end has no criterion (limit)
by which anyone would say that [he is or is not] — for him it doesn't exist.
When all phenomena (dhamma) are done away with,
all means of speaking are done away with as well.
This last verse is equally true of anyone who is no longer obsessed with and attached to the phenomenal aggregates. SN 22.36: Bhikkhu Sutta, states:
"Monk, whatever one stays obsessed with, that's what one is measured by. Whatever one is measured by, that's how one is classified. Whatever one doesn't stay obsessed with, that's not what one is measured by. Whatever one isn't measured by, that's not how one is classified."
"I understand, O Blessed One! I understand, O One Well-gone!"
"And how, monk, do you understand the detailed meaning of what I have said in brief?"
"If one stays obsessed with form, lord, that's what one is measured by. Whatever one is measured by, that's how one is classified.
"If one stays obsessed with feeling...
"If one stays obsessed with perception...
"If one stays obsessed with fabrications...
"If one stays obsessed with consciousness, that's what one is measured by. Whatever one is measured by, that's how one is classified.
"But if one doesn't stay obsessed with form, lord, that's not what one is measured by. Whatever one isn't measured by, that's not how one is classified.
"If one doesn't stay obsessed with feeling...
"If one doesn't stay obsessed with perception...
"If one doesn't stay obsessed with fabrications...
"If one doesn't stay obsessed with consciousness, that's not what one is measured by. Whatever one isn't measured by, that's not how one is classified.
"Lord, this is how I understand the detailed meaning of what you have said in brief."
"Good, monk. Very good. It's good that this is how you understand the detailed meaning of what I have said in brief.
And again, clearly and succinctly emphasizing the practical application of dispassion toward mental perceptions and disidentification through discernment, the Buddha teaches in Sn 4.9: Magandiya Sutta:
For one dispassionate toward perception there are no ties;
for one released by discernment, no delusions.
Those who grasp at perceptions & views
go about butting their heads in the world.
Well said.