So, let's say, Koy was an adult when Shigaraki was a kid.

Just trust the process, please, it'll be great. 
(Also spoilers if you haven't seen season 5, read at your own risk)

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Tenko was wandering the streets, just killing his family...He was slightly bloody and was in a state of shock. He tried asking for help, but everyone just walked by, no one even attempting to help him. At least, at first.

Tenko was sitting in an alleyway when these three men tried kicking him out. "Hey! This is our turf, brat!" One said, kicking him down. The three roughed up the boy when one of them got pinned to the wall with a piece of stone. "Step away from the child, and I won't hurt you..." a deep voice said. They all turned and saw the number 5 hero, Ground Breaker. "Oh shit, let's get out of here!" The other thug said, trying to run away, but Ground Breaker trapped them. "No no no, that's not how this works," Ground Breaker said, keeping them in place. "You'll be going straight to the police..." He then looked, and saw the blue-haired boy, seeing he was afraid. "Hey, it's okay, buddy," he said, holding his hand out to him. Tenko was hesitant, about to take his hand, but then stopped. "I...I don't want to hurt you..." the boy said, Ground Breaker was slightly confused, but was patient. "Then how about I pick you up, okay?" he said, reaching down and slowly picking up the child, keeping him safe.

Ground Breaker had turned the three criminals into the police, having brought Tenko with him, to see if he could find his family. "What's your name, little man?" he asked with a gentle tone. "...T-Tenko Shimura..." Tenko said quietly, and Ground Breaker's smile faded. He had heard what happened to that family. The worst of it, he was on patrol in that neighborhood, and when he heard the screams, he was too late to save anyone. "Oh...I see, stay here real quick, alright?" Ground Breaker said, before going up to the police officer at the desk. "This kid...he lived at the Shimura household...his family was killed in the incident," he told the officer. "What can we do to help this kid?"

"We can put him in foster care, or drop him off at an orphanage, but other than that, we can't help him, besides, look at him, no one's going to want that kid."

"Why? Because he's traumatized? Or because he looks a certain way...?"

"I-I didn't mean anything bad, Ground Breaker, I just-"

"If you really think that, then I'll take him in, and raise him as my own."

"But...he's just some random kid."

"Every child deserves a home. Officer..." Ground Breaker walked away from the front desk, going up to Tenko. "Hey, come with me, I'll take you to your new home," he said with a smile, holding his hand out to him. Tenko looked at his hand, reaching out, but then stopped. "I...I'll just walk next to you..." he said, standing up. Ground Breaker sighed, he thought he didn't trust him, which he could understand, but didn't want him to be afraid. 

Ground Breaker took Tenko to his home, where he would take care of the young boy. For a few months, Tenko was timid and hesitant around Ground Breaker, also known as Koy, and he was very patient with the boy, not trying to rush him to trust him. One day, Tenko went to Koy, wanting to talk about his quirk for the first time.

"Mr. Koy...I have a bad quirk..." he said, looking at his hands. Confused Koy went up to him, crouching down to his level. "What makes you say that, kid?" 

"...I killed my family with it...I didn't mean to...I...I'm the reason it came crumbling down..." Tenko started to cry, his hands shaking. Koy's eyes widen for a moment but softened. "...Was it your first time with your quirk, Tenko?" he asked, reaching for his hands. Tenko took a step back. "D-don't touch my hands!" he yelled, looking at Koy with teary eyes. "I...it'll kill you..." Koy then realized why he never let him hold his hands. "Wait here, okay?"

Koy left the room for a moment, before coming back with a pair of gloves. "These were supposed to match my hero outfit, but I accidentally put them through the dryer, but they seem perfect for you," he said with a smile, helping Tenko put the gloves on. "Okay, hold my hand now," he said, holding his hand out.

Tenko slowly reached his hand out, holding Koy's hand. He closed his eyes, afraid of what will happen. He opened his eyes, seeing that...nothing happened. "See? I'm okay, we'll have you wear these until you can control your quirk, okay?" Koy said with a gentle smile. Tenko looked, seeing that the gloves kept Koy safe. He then went and hugged Koy close. "T...thank you...you're my hero..." Koy stood there frozen, before hugging him back. "Thanks..." 

As the years went by, Koy helped Tenko control his quirk, when to use it, and when to keep it under control. Koy raised Tenko to be one of the best people around, and at one point, Tenko started to call him dad. When Tenko was 14, he said that he wanted to become a hero like Koy, so he helped him train for the UA entrance exam. 

"Alright, you ready for this, buddy?" Koy asked, walking Tenko up to the main gate. "Yeah, I'll make you proud, Dad!" Tenko said with excitement, smiling happily. Koy chuckled, ruffling his hair. "Alright, break a leg, I'll try to pick you up right after, I have patrol." 

Koy waved to Tenko, and the two went two different ways. Tenko went in, getting the information about the exam and how they'll have to destroy some robots and the point system they had. As the students went in, Tenko was crushing it. He destroyed robots with his decay, as well as protecting others and making sure no one got hurt, even destroying some of the robots that weren't worth points because he didn't want anyone hurt. He had done very well, proving to be a great hero. 

After the exam, he was walking out with a smile on his face, he was excited to tell Koy about it, when he saw one of his sidekicks. "Tenko...something's happened..." 

"Huh? What do you mean?"

"It's...It's Koy...he's in the hospital..."