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Izuku, ever since he first entered U.A, he suddenly kept finding glowy gold-colored fragments. It became some sort of 'hobby' for him, always picking them up whenever he finds them and keeping the broken fragments in a jar.
Until one day, he picked up what he believed was 'another' piece which was final. It was the last piece of which he had found outside of U.A. in the garden. he ended up putting the piece in the fragments jar, for safekeeping until he finds other pieces. But suddenly, the jar shook, his eyes focused on it once he's in his room. He noticed how the fragments pieced together and formed into a beautiful glowing star in the color of gold.
His green eyes emitted a gentle emerald glow as a result of the illumination of the star's light in his dark room. But he took notice of the star's shaking inside the jar as if was trying to escape and return back to its original owner.
He was so unsure of what is going on, but the star flew out of the jar, and he chased after it, using his blackwhip to swing around and follow the fast ray and string of light the star gave off. He never knew that it was tracking you. You were a person in some unknown prophecy that his mentor, Gran Torino, had kept from him. The prophecy was that you were meant to accompany the holder of One For All and defeat All For One.
But Izuku was unaware of that prophecy being a thing. And he kept following the star until it saw it hover over an alley, crashing down and reacting to your body.
He landed behind you, confused and shocked. The star looked as if its glow was vibrating, reacting to you. The star was simply attached to your back.