I've been wondering about that for ages, too. To be honest, I can't see her (or anyone else of her age, intelligence and common sense) opening the door to someone they don't know with a kitchen knife. No matter how scared, if you open the door with a knife, unless you are a knife fighter, it's unlikely you'll be able to use it properly in self-defence. It turns you into a danger to yourself because chances are the knife will be used against you, or you'll hurt yourself trying to use it. Miss Y. wasn't in the habit of engaging in knife fighting, as far as we know.
Given that she was uncomfortable about being on her own (which I can totally understand), why would she have opened the door to someone she didn't know (or only may have only known by sight, given that they were neighbours) after dark, after seeing him through the kitchen window (if that's what happened first), when she was on her own and not overly relaxed about it? The only thing I can come up with (meaning, the only reason *I* would open the door in such circumstances) would be if a neighbour I knew by sight indicated (say, through the kitchen window) that he'd taken a parcel in for me (it wouldn't have occurred to me to look for a Royal Mail notification card etc., especially if he'd surprised me) or that he'd brought my cat, or some such likely thing that neighbours might do.
I am so sad about the whole thing. A life taken so unneccessarily and in such a horrible way. My heart goes out to her family and friends.