Muzan Kibutsuji was dead- dying at the hands of The Demon Slayers after warring with them for over 1000 Years. When he died, he knew full well that he was never going to reincarnate... or so he believed! After an untold amount of time in the void, a strange voice gave him a choice, remain in the void for the rest of time? Or... become reborn. He chose the latter.
Muzan Kibutsugi was dead, and would never reincarnate due to his status as a Demon and because of his actions. Or at least, that was what everyone thought. While Muzan would never get the chance to truly live again, he could always make sure his legacy carried on in an event of a rebirth... (OP!Izuku, MorallyGrey!Izuku, Demon!Izuku, HeavyCanonDivergence)