the 'Perfect One', lit. the one who has 'thus gone', or 'thus come', is an epithet of the Buddha used by him when speaking of himself.
To the often asked questions, whether the Tathāgata still exists after death, or not, it is said (e.g. S. XXII, 85, 86) that, in the highest sense (paramattha, q.v.) the Tathāgata cannot, even at lifetime, be discovered, how much less after death, and that neither the 5 groups of existence (khandha, q.v.) are to be regarded as the Tathāgata, nor can the Tathāgata be found outside these corporeal and mental phenomena. The meaning intended here is that there exist only these ever-changing corporeal and mental phenomena, arising and vanishing from moment to moment, but no separate entity, no personality.
When the commentaries in this connection explain Tathāgata by 'living being' (satta), they mean to say that here the questioners are using the merely conventional expression, Tathāgata, in the sense of a really existing entity.
Cf. anattā, paramattha, puggala, jīva, satta.
A commentarial treatise on "The Meaning of the Word 'Tathāgata' " is included in The All-Embracing Net of Views (Brahmajāla Sutta), tr. Bhikkhu Bodhi (BPS).