True, in conventional language we use labels to refer to people:
“Just as, with an assemblage of parts,
The word ‘chariot’ is used,
So, when the aggregates exist,
There is the convention ‘a being.’ SN5.10
And when there is an enlightened being, there is the convention ‘a Tathagata,’ or ‘an arahant,’ or whatever.
But in this context it means something deeper than the conventional term. It means there is no such thing or Self which is the Tathagata.
Also helpful is to know that other religions seem to have used the same term to refer to their idea of enlightenment, definitely the Jains, whose text we do have use a nearly identical term. But to them it referred to a liberated soul. If you’d say ‘Tathagata’ it meant a soul to them. To the Buddha it was just a conventional word, nothing real. So it didn’t really exist as a thing itself, whether before or after death.
“Is it really true, Reverend Yamaka, that you have such a harmful misconception: ‘As I understand the Buddha’s teaching, a mendicant who has ended the defilements is annihilated and destroyed when their body breaks up, and doesn’t exist after death.’” […]
What do you think, Reverend Yamaka? Do you regard the Realized One (Tathagata) as form?”
“No, reverend.”
“Do you regard the Realized One as feeling … perception … choices … consciousness?”
“No, reverend.”
“What do you think, Reverend Yamaka? Do you regard the Realized One as in form?”
“No, reverend.”
“Or do you regard the Realized One as distinct from form?”
“No, reverend.”
“Do you regard the Realized One as in feeling … or distinct from feeling … as in perception … or distinct from perception … as in choices … or distinct from choices … as in consciousness?”
“No, reverend.”
“Or do you regard the Realized One as distinct from consciousness?”
“No, reverend.”
“What do you think, Yamaka? Do you regard the Realized One as possessing form, feeling, perception, choices, and consciousness?”
“No, reverend.”
“What do you think, Yamaka? Do you regard the Realized One as one who is without form, feeling, perception, choices, and consciousness?”
“No, reverend.”
“In that case, Reverend Yamaka, since you don’t acknowledge the Realized One as a genuine fact in the present life, is it appropriate to declare: ‘As I understand the Buddha’s teaching, a mendicant who has ended the defilements is annihilated and destroyed when their body breaks up, and doesn’t exist after death.’?”
“Reverend Sāriputta, in my ignorance, I used to have that misconception. But now that I’ve heard the teaching from Venerable Sāriputta I’ve given up that misconception, and I’ve comprehended the teaching.”
“Reverend Yamaka, suppose they were to ask you: ‘When their body breaks up, after death, what happens to a perfected one, who has ended the defilements?’ How would you answer?”
“Sir, if they were to ask this, I’d answer like this: ‘Reverend, form is impermanent. What’s impermanent is suffering. What’s suffering has ceased and ended.
Feeling … perception … choices … consciousness is impermanent. What’s impermanent is suffering. What’s suffering has ceased and ended.’ That’s how I’d answer such a question.” SN22.85