In the final scene of Angel Beats!, we see what we know is Otonashi pass by Kanade. Kanade is humming Iwasawa's last song 'My Song', which she wrote in the afterlife.
How did both Otonashi and Kanade remember this song? If they disappeared in the afterlife, their souls/spirits would have passed on, so how do they remember it?
I assumed that when they are 'reborn' in their next life, they would have no memory of the afterlife or previous life. I guess this isn't the case.
There could be a few explanations but I don't think it goes that deep. The idea for the anime did imply that their souls kind of ended up in that world temporarily and then, they left eventually. It's the same soul of the same person. There's no telling how do our memories actually act.
There is a hell lot of stuff up there in your subconscious but you are not aware of it. You only remember what is in your conscious part of brain. The rest of subconscious is vast and still there but only in a dormant form. You don't really know what it is. It is depicted in dreams and some abnormalities.
It's quite possible that the memories keep accumulating in one's subconscious as he goes through life.
Have you ever had a tune stuck in your head but you have no idea where it came from? The tune just came to you like you have known that little tune for your whole life? I think that's what the author was going for.
I also think the song itself could be etched into their soul, because they may not remember anything but maybe their soul remembers the strong feelings?
These are just the ideas I made up when I saw the ending...
I agree with the fact that it might not be as deep as having the song etched in their soul but it could be that one of them heard something that triggered that memory of the song and not where it came from and when otunashi heard it it triggered an aha moment along with the memory of kinade and that's why they both remember that song.
