Great question — answering as the UphillTech team:
The way I've always read that scene is that she fell, but did not die. She did however suffer severe trauma. The larger part of that trauma was to her psyche. An oft used story telling instrument in movies is the personality switching trauma. This happened to Selina when she fell, it changed her into a more assertive character. Having the cats around her when she woke up as the new Selina "impressed" on her mind a more feline personality. Not only is she more aggressive and independent, she also moves and acts more like a cat. You could say that the trauma to her head made her more than a little bit 'insane'.
Full answer by System Down: https://movies.stackexchange.com/a/2031 (CC BY-SA 4.0).
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