It was decided that despite Izuka being almost in perfect health physically, she was to remain in hospital for a few more days just to ensure there were no problems that the Doctors had missed. Izuka didn't mind too much, but she was rather afraid of any doctor that came towards her with a syringe or anything that looked remotely like surgical tools. All-Might, officially introducing himself to the Midoriyas as Toshinori Yagi, remained in the Hospital too while the Doctors decided if he'd need any medication to help with his new weakness. In his Muscle Form, All-Might was as powerful as ever, though he found it a bit harder to maintain it, but in his normal form he had slimmed down. He was still very fit and athletic, but his build appeared leaner and less muscular.
Izuka was also remaining in hospital until after she'd had her first Psyche Exam, and to get new accommodations prepared for her since her story had broken in the Media.
The Story of Izuka Midoriya, kidnapped child whom was recovered a year later was a massive story, with the public pouring attention into the news. The story was edited to give credit for the Villain's demise to All-Might (done at Inko Midoriya's request) and news of Izuka's quirks were kept completely confidential, edited down to a Fire and Healing quirk. Her saving All-Might's life WAS left in the story though and the general public were practically trampling over each other to praise her. The Government had opened a small fund to help the Midoriya family through the stressful time and the Public had donated so much money that Inko had to hire an accountant to help deal with it, and an entire office at the local government office had been converted to a screening room for letters and gifts sent to the family.
Saving the Number One Hero was a big deal it seems.
Of course, Izuka didn't seem to care much; she was just so happy to be home, and on the second day of her Hospital stay, things got better when the Bakugou family came to visit.
Izuka had just finished her breakfast, which she spent listening to stories from All-Might and her mother, when she heard a loud and very familiar voice.
"GET THE HELL OUT OF MY WAY! MY FRIEND IS IN THERE!" screamed a youthful male followed by a sandy haired ten year old boy charging into the room, quickly followed by a pair of doctors and a young couple with similar features to the boy.
"Kacchan!" Izuka yelled, joyful tears spilling from her eyes. She hopped out of bed and ran towards the boy.
Katsuki Bakugou, better known as Kacchan by Izuka, grinned and met the girl halfway, capturing her in a tight hug. "DEKU! Er, I mean, Izuka!"
Izuka giggled, "It's okay, you can call me Deku! I'm so happy you're okay! After what the villains said, I was afraid they'd come for you again!"
Katsuki's grin turned into a sad smile, "Damn Deku... no quirk and yet you still saved my ass." he muttered, a long standing pain lacing his words.
Mitsuki Bakugou, Katsuki's mother, knelt down and hugged the two children while Masaru, his father, stroked the girl's hair. "Izuka, that creepy feathered guy Nest told us everything that happened. He said you'd need support from Katsuki, so we had to be told."
The usually strong and fiery woman broke down in tears; "You silly child... you saved my baby's life. If they'd taken him, he'd have lost his quirk and been killed, or turned into one of those freaks. But you saved him, even though you got tortured... I'm sorry I didn't keep a better eye on you two, but thank you so much for saving my boy!"

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The Immortal Hero: Phoenix
Fanfiction9 Year Old Quirkless Girl Izuka Midoriya is kidnapped by villains and held captive for a year. Saved by All-Might, Izuka is discovered to have a Quirk that gives her the power of a Phoenix, including returning to life after being killed. With All-Mi...