In Theravada the issue of what remains of an enlightened person after they die seems to me to be usually left very vague, whereas in the Mahayana, Bodhistattvas and Buddhas are, it seems to me, considered to still exist as individual beings, though perhaps dwelling in other realms etc. Is that a fair comment? And if so, if, as is often said, there is no true individual self - it is just a collection of aggregates that moves from life to life etc.. - then what is left to constitute their individuality, once all delusion has gone?
I think that logically that there has to be at least some form of individuality after Enlightenment happens. I say that based on examination of the one example of Enlightenment that all Buddhists agree on, Buddha Shakyamuni.
Even though there is lots of disagreement in regards to what he taught there are some things that everyone seems to agree on. He did mundane things like walk from place to place, talk, eat food, etc. In order to do mundane things like that there would have to be at least some form of individuality, otherwise he wouldn't be able to do mundane things as there would be no distinction between Shakyamuni, the road he walked on, the people he talked to, or the food he ate.
How he interacted with/the exact nature of this individuality is very much up for debate but unless you question the existence of historical Buddhas the fact that there had to have been individuality there in at least some sense of the word is pretty definite.
I'm an agnostic in the same sense that Robert Anton Wilson was, except his reaction was laughter. Mine isn't.
I am not a teacher in any tradition, Buddhist or otherwise. Anything that I have posted should not be taken as representing the view of anyone other than my own. And maybe Larry S. Smith of Montgomery, Alabama. But most likely just me.