Think about it. Those who dare to stop Kira are declared as evil; well, Misaki's father is an example, so Light has killed him when Misaki is a kid.
When the real Misaki is seen, she is in a suspended chamber. Her transformation into a Ghoul appears to be a messed up reality. By the way, the hallucinations justify this.
It is revealed that after failing the academy for acting like a ditz, she begins to search for help and finds a program that involves into going into a suspended chamber. As a result, she commits suicide and her body is placed in that chamber, triggering the events.
Even though the glitch can be fixed, Misaki has to decided whether to continue living in a dream or back to reality. For the latter, she has to be killed.
Misaki has been dead all this time.
It turns out that a Ghoul has managed to kill Misaki and has taken over her body. However, at some time, it begins to have redeeming qualities.
killed Misaki's father.
Maybe he's involved with catching Lucy before Misaki is born?