I generally don't respond to her personal details. I usually am looking at the ground or the opposite side of the room she is in, and let her talk. Once she told me how she'd fainted at an aiport because of her eating disorder, and i spontaneously said "Wow, that is scary!" to which she agreed.

I don't think she's looking for a response necessarily, it is probably intended to help you foster a connection with her or some therapist-y thing like that.