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"Izuku" (Deku) Midoryia:
-All might wasn't there to save Izuku during the sludge villain attack. Just like in TSHD the sludge can go through the memories of its host and attempt to copy the behavior as best as possible, except it does have experience as a person because the sludge is just another person's quirk.
-"Izuku" has a quirk now. That quirk being Sludge. It's a lot like black whip except he needs to be more focused while using it. He can make the sludge soild if he tries hard enough but only for a few minutes. It can go through any crack and would be good for search and rescue missions. "Izuku" can feel what happens to the sludge ropes but it's very dampened. If the sludge gets destroyed or hurt "Izuku" feels a sting or burning sensation depending on what happened to it. If "izuku" begins to freak out and panic or lose consciousness from an injury then the body begins to lose form and leaks sludge.
-Izuku's body is preserved due to the sludge quirk. When "Izuku" loses control for a while the body begins to look dead [gee wonder why] (Pale, ashy, empty bloodshot eyes,).
-The Sludge Villain has never tried to look through all the memories of its host before Izuku. Therefore not knowing that once it did so and began to copy izuku "perfectly" that it would forget what it used to act like and its previous behaviors. Turning itself into a new Izuku. (Kinda like The City of Blank)
-Katsuki does figure out what happened to Izuku fairly soon after the attack and is horrified by what happened. Consumed with grief he keeps "Izuku" close to him and is always trying to be better towards him. No one else knows why Katsuki is acting so different around "Izuku" because he can't tell anyone what happened. After all, having a strange version of Izuku is better than not having him at all. Right?
-Just to clarify one more time, The Sludge Villain is basically an uncanny valley version of Izuku now. Everyone gets a strange sense of paranoia when around him but no one can figure out why.