(Trigger Warning. This HeadCanon mentions abuse. Don't like, don't read.)

Kokichi was abused and then abandoned as a child. His parents would ignore him constantly. And when they weren't ignoring him, they were throwing insults at him and beating him until his body was a bloody raw red color. Then, his parents decided enough was enough. They gave him up to an orphanage. Kokichi met Maki at that orphanage. You see, things weren't much better there and he was sick of being constantly treated like dirt. Maki agreed with him. She hated being treated like dirt as well. In fact, they were so fed up with it they made a plan to run away. But here's the thing, Maki was taken to become an assassin the night they were going to execute the plan. 

Ouma was hurt, but understood. He decided to execute the plan anyways, he did it in the name of his mother figure at the orphanage, Maki Harukawa. While Kokichi was on the run, he met the soon-to-be members of D.I.C.E. They were all in a situation regarding family and abuse, and that's what they bonded over. Once ever single member met, Kokichi suggested they form D.I.C.E. They all agreed and that how Kokichi became the SHSL Supreme Leader. He lied and stole to get food for his new found family, but he always said he lied and stole for greedy reasons, so no one thought he was weak.

Maki and Kokichi met up again a few years later. Ouma told Maki all about D.I.C.E and when she heard about how he ran away, she thought Ouma betrayed her and that's why Kokichi and Maki have some bitter feeling toward each other. But, why do they remember each other in the game if they're memories were washed? Maki and Kokichi were slowly gaining they're memories back. Why and how? Nobody knows. After the game ended, they made up and decided to push away their past history together and try to become friends. Now, in the present, they actually have a good brother-and-sister relationship, but they're both will never fully heal from they're past.