No I don't, not at all.
The only thing I've ever asked about was her illness when she went out for surgery and expected to be out for some time. It turned out she was not thank goodness. When I asked she gently said that she had made the decision to not share that at this time. That was okay with me; mostly I just wanted her to know I cared about her. That was the session she allowed me to hug her.
I don't want to know the details of her life. I know she is a candidate at a psychanalytic institute and that she has been a therapist for 20 years and she has a daughter. I don't want to know any more. I want her to kind of just exist in that room for me, for now at least. That's all I need to know
She knows I don't ask intentionally because I understand that disclosure is not something neither of us want.