All For One lies on his deathbed. The fight with his nemesis, the 8th holder of his brother's quirk, had left him in a bad state. He had several regeneration and durability quirks, but the damage had overwhelmed him. He couldn't see, eat or walk. He could barely talk or move. It was his time to go. But the legacy shall continue, within his son Izuku.
Or, Izuku is the son of All For One and has the same quirk. Just before the villains death, Izuku is given most of the quirks in AFO's arsenal. Alongside a few quirks he stole himself, he continues the name of All For One.
Izuku Shigaraki, younger brother to Tomura Shigaraki both boys are the son of Hisashi Shigaraki, AKA All For One. Tomura has his decay quirk and training to gain All For One from his father. Izuku on the other hand, his quirk is an upgraded version of All For One, he's more powerful than his own father. Izuku is also able to act like an innocent cinnamon roll even though he could be mistaken for the devil himself. The brother duo, is absolutely horrifying when working together. Izuku has white hair and grey eyes but when his quirk is activated his eyes go from grey to crimson red matching his older brother.