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When an individual has given up craving and the conceit of 'I am' their mind is liberated, they no longer come into any state of 'being' and are no longer born again.
The Aggivacchagotta Sutta records a conversation between the Buddha and an individual named Vaccha that further elaborates on this. In it Vaccha asks the Buddha to confirm one of the following, with respect to the existence of the Buddha after death:
After death a Buddha reappears somewhere else
After death a Buddha does not reappear
After death a Buddha both does and does not reappear
After death a Buddha neither does nor does not reappear
To all four questions, the Buddha answers that the terms 'appear', 'not appear', 'does and does not reappear' and 'neither does nor does not reappear' do not apply. When Vaccha expresses puzzlement, the Buddha asks Vaccha a counter question to the effect of: if a fire were to go out and someone were to ask you whether the fire went north, south, east or west, how would you reply? Vaccha replies that the question does not apply and that an extinguished fire can only be classified as 'out'.
