Mika = white, Fumi = black hair
Mika 'died' as Fumi didnt need her anymore and 'killed' her. Fumi thought she was strong enough to live her life on her own and she didn't fly, went emo, tried to kill herself.
This brings back the split personality of Mika, who stops Fumi. She explains how she felt responsible for all the bad things and just wanted to make Fumi happy and thought she had to disappear for shooting her father and the whole coma business when she took control of Fumi.
They then reconcile about how they both love each other, both wanted to live normal lives and each were basically doing things they thought the other would want to be happy and both made each other miserable. This leads to the bawwwwinng scene in the OP.
From there, Mika returns to shigofumi duty due to the clause in the books that the hot red head shigofumi friend found with random library clerk shigofumi person. This is never really explained and seems left open for a sequel, much like the confession scene where we didn't get an answer from the guy.
In the end, Mika lives her life as shigofumi, Fumi returns to school and regular life and won't let her split personality take control of her life again, as evidenced by the passing by scene at the very end. She doesn't really hate Mika, just that weak part of herself.