let's get into some big headcanons and break down his backstory. i've summarized it as simply as i can but this is still a little long, sorry!
Hazuki is half-Korean and he was born and raised in Shinjuku. He lived in Ōkubo (also known as Shin-Ōkubo) - a neighborhood located within the district near Kabukichō - and attended school there.
He would frequently make trips to Shibuya and Harajuku because he lived near the Higashi-shinjuku station.
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Hazuki used to have a big personality. He was rebellious, a risk taker, he had a silly but also a morbid sense of humor, he took up space where he wanted to, he got angry fast but loved really hard, he was intense, he was gloomy, but he wasn't afraid to share his laughter. As he is right now, who he was is basically gone, but only almost. More below.
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He had a hyperfixation on CAT when he was alive, a passion since abandoned now that he's a cog in the machine for the Higher Plane. Yay.
He used to have a big collection of CAT merch, he'd often blow what little allowance he had on the things CAT made. CAT gave him the escapism he needed in a life where he felt like an outsider, had an abusive home life, and suffered from severe depression. Which leads me to...
DISCLAIMER; This isn't a theory, it's just a personal headcanon for my take on Hazuki, to add a little spice and give him a deeper connection to the story. It isn't an exclusive headcanon to any particular portrayal of Neku. You also do not have to abide by it, I can disconnect this portion and fill in the blank.
Hazuki is Neku's dead best friend, and what I've built about him thus far is built strongly around what Another Day (This Day Ends with You!) Neku tells us about him;
"I wouldn't have found the mural in Udagawa if he hadn't told me about it. He was my one real friend--the only guy in my class I could talk to as an equal. I was fine with that. Just him and me. Man, I miss him... Not that I have a right to... Not after I killed him. I'll never forget that day... We were set to meet up at the usual spot. I asked him to come. I was waiting in front of the CAT mural... but he never came. Only later did I hear about the accident. I was so mad. Then I felt awful... I shouldn't have asked him there. If not for me, he'd still be here... It's like I killed him."
I haven't decided how Hazuki died yet, exactly, but it was a genuine accident. Hazuki's memories of Neku are intact, as is his attachment to him. So why did he choose to remain dead after completing his Reaper's Game in Shinjuku?
Hazuki has an extraordinary Imagination. He was offered ascension into the Higher Plane and accepted it. During his Game, he learned about how Reapers could travel into the RG and made the assumption that he would have the same freedom awaiting him as an Angel, giving him the escape from his life and control that he craved while still allowing him to be with Neku.
It was not to be, though. He became trapped in the Higher Plane while small pieces of him were altered in order to assimilate him into the Hive Mind of the Angels.
However, lot of his rebellious nature remained intact and he often resisted the control of the Angels, resulting in a push back of more alterations, brainwashing, and eventually a push to make him Composer of Shinjuku, while the Angel in charge of his assimilation became his Producer. It was an attempt to straighten him out by giving him a responsibility, and it was an execution of the current Composer. It was also meant to be seen as a "positive" thing, a show of trust, of love, because you can't have all bad and expect loyalty to hold.
Pretty obvious, I feel, but Hazuki has a bad relationship with his Producer, they do NOT like each other.
Chewing up headcanon and canon together; Hazuki never actually wanted to be Composer, and he didn't feel any remaining love for Shinjuku. Seeing it already as a flawed place, he quickly and coldly made the decision that Shinjuku was unfit and needed to be Purified. It was shortly before Neku was dragged into being Joshua's proxy that Hazuki's own conflict with his Conductor began, who he did not give the same fair chance to that Joshua gave to Megumi.
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I also like to think that Hazuki's disconnection from the lower planes and his humanity became more severe in the time it took for NEO's Reaper's Game to conclude.
hazuki is joshua's opposite to me, he's the cute little negative character development to joshua's positive character development, and also neku's.
but i'm crafting this story with hazuki having the chance to go any way in terms of development, but in his primary story he will be saved and he will get better and it will be beautiful. yay. he isn't lost forever, he's just trapped himself. he royally screwed himself over and took everyone down with him LMFAOOO
and that's it for this current session of clearing out my gay little braincage. i have so many more thoughts but i'll save them for more posts so this doesn't get too long.