Which is ironic, considering she's the one who murdered her.
Honestly, there doesn't seem to be a difference between the normal BRS and the Insane BRS -- either way, she's trying to kill any Otherself in sight. It's just that now Mato is trapped inside of her.
So, anyway. Yu and Strength were apparently the first, and Strength was born from Dissociative Identity Disorder; an alternate persona that Yu created to distance herself from her pain. How Yu got in contact with the Otherworld is unknown -- it certainly isn't normal.
She's the catalyst who creates Black Gold Saw or otherwise wakes Saya up to her existence. Then Yu and Strength apparently switch places.
Even as Strength, Yu doesn't want to fight, so she appoints Black Gold Saw to protect her in the Otherworld. While Black Gold Saw gets into fights and otherwise meddles in things, Strength keeps far away from anyone. The only thing she does is haul away Othercorpses, until she rescues Saw and starts fighting Insane BRS.
Was Black Rock Shooter the reason why Yu wanted protection in the Otherworld? Was Shooter already going around killing Otherselves? If not, why were she and Black Gold Saw fighting before Mato and Saya ever met?
Why did Strength, posing as Yu, seek out and befriend Mato? Odds are, Strength singled Mato out specifically because of Black Rock Shooter.
Was Strength hoping to stop BRS by putting Mato in control?
What about Shooter's own motivations? Why is she killing Otherselves even when Mato explicitly doesn't want her to? When Shooter spoke with Mato, was she lying to her real self, tricking her into a trap that would grant BRS more power?
Why do Otherselves leave corpses, anyway? In a world like the Otherworld, wouldn't the corpses vanish just like landscapes without owners?
And why does Yu bother disposing of them? Would they rot, or spoil the environment? Why should she care? Is it not a sort of mental world where space and location are mere suggestions? She has her own territory and the territory of every other mind in the world and whatever common ground exists between.