I'd never carry my passport in a purse. Far too risky. I actually sew extra pockets into my trousers with a hidden zip (hidden inside another pocket) to the pocket that holds my passport. I need about 3 hands to get it out of there, but that means that no-one else can get it out either.
I also keep emergency cash and a spare credit or ATM card in there. Pickpockets are welcome to grab my wallet.
Audrey