Yoshida, after learning from Fami about the Falling Devil attack, told his Buddy Fumiko to go help because he didn't think he would be able to get there in time??? Fumiko chose to save CSM rather than waste her life like all the other Devil Hunters and PS agents, cause CSM could win???
I think that's just a standard government issued knife all public safety workers have. I still think the mystery blood feeder was Yoshida, otherwise Denji would have recognized Fumiko later. If a woman gave him blood he would have remembered and also hit on her when it happened.
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In which case she might be way older than we think, and a pawn public safety has had for decades. Hence her "promotion" despite being a complete bum