As you may know, Kuro is a complex character, especially if we take away the fanservice, as she has a huge existential problem being the original Illya who was sealed and denied to exist, remaining as a secondary personality of Illya. She got angry with Illya when she accidentally denied her existence by saying she didn't want to be a magical girl. Kuro went so far as to want to kill Illya and almost disappeared, but Illya convinced her to live knowing that her purpose in the Holy Grail War will never return. Also, she often questions whether or not she deserves to exist.

She is also fused with the Archer card, which is problematic, as it comes from Emiya Archer, who also has a huge existential problem: he is someone who doesn't love himself and hates the fate that befell him, full of regrets. So much so that he traveled to the very war he participated in with the desire to kill his younger self, in order to cease to exist, despite the fact that he is outside of space and time, and nothing would change. Kuro, being linked to the Archer card, would disappear if Emiya Archer ceases to exist. Unintentionally, Emiya denied Kuro's existence, as the Archer card is currently the core of his existence.

Fate (the character in Nanoha , not this franchise) is also in this official crossover too