There is a related sutta, SN44.6 that says:
"For one who loves form (and the rest of the five aggregates), who is
fond of form, who cherishes form, who does not know or see, as it
actually is present, the cessation of form, there occurs the thought,
'The Tathagata exists after death' or 'The Tathagata does not exist
after death' or 'The Tathagata both exists and does not exist after
death' or 'The Tathagata neither exists nor does not exist after
death.'
"But for one who doesn't love form (and the rest of the five
aggregates), who isn't fond of form, who doesn't cherish form, who
knows & sees, as it actually is present, the cessation of form, the
thought, 'The Tathagata exists after death' or 'The Tathagata does not
exist after death' or 'The Tathagata both exists and does not exist
after death' or 'The Tathagata neither exists nor does not exist after
death' doesn't occur.
"For one who loves becoming, who is fond of
becoming, ...
"But for one who doesn't love becoming, who isn't fond of becoming ...
"For one who loves clinging/sustenance ...
"But for one who doesn't love clinging/sustenance ...
"For one who loves craving ...
"But for one who doesn't love craving ...
I have heard another story about a master saying "think about monkeys", and the meditator thinks about monkeys with his eyes closed. After this, the master says "don't think about monkeys", and again, the meditator never fails to think about monkeys with his eyes closed. Why? Because in both cases, he has an obsession with monkeys.
Similarly, views about whether 'The Tathagata exists after death' or 'The Tathagata does not exist after death' or 'The Tathagata both exists and does not exist after death' or 'The Tathagata neither exists nor does not exist after death' all occur only if one has an obsession with the five aggregates, becoming, craving and clinging.
Similarly, having views about whether one (the self) 'exists after death' or 'does not exist after death' or 'both exists and does not exist after death' or 'neither exists nor does not exist after death' are all due to obsession with the five aggregates, becoming, craving and clinging.
The Acela Sutta shows that the Buddha teaches the Right View using dependent origination, rather than eternalism or annihilationism. (This comes from here but the full text can be found here):
Again, when the Buddha was asked by the naked ascetic Kassapa whether
suffering was of one's own making or of another's or both or neither,
the Buddha replied "Do not put it like that." When asked whether there
was no suffering or whether the Buddha neither knew nor saw it, the
Buddha replied that there was, and that he both knew and saw it. He
then said "Kassapa, if one asserts that 'He who makes (it) feels (it):
being one existent from the beginning, his suffering is of his own
making,' then one arrives at eternalism. But if one asserts that one
makes (it), another feels (it); being one existent crushed out by
feeling, his suffering is of another's making,' then one arrives at
annihilationism. Instead of resorting to either extreme a Tathaagata
teaches the Dhamma by the middle way (by dependent origination)"
(S. XII, 17/vol. ii, 20).
The Yamaka Sutta also speaks of an interesting notion:
"Then, friend Yamaka, how would you answer if you are thus asked: A
monk, a worthy one, with no more mental effluents: what is he on the
break-up of the body, after death?"
"Thus asked, I would answer, 'Form is inconstant... Feeling...
Perception... Fabrications... Consciousness is inconstant. That which
is inconstant is stressful. That which is stressful has ceased and
gone to its end."
"Very good, my friend Yamaka. Very good.
So, rather than saying that after Parinibbana, the Buddha exists or does not exist, it's better to say suffering has ceased and gone to its end.
In a similar way, rather than saying that after death, whether an unenlightened person is non-existent or existent or reborn or not reborn, it's better to say that suffering has not ceased. And what happens when suffering has not ceased, is understood using dependent origination.