The person asking an intimate question should leave room for an answer that does not disclose.

Asking about children, money, illness or a marriage can be entirely warm and still put somebody in a corner. Once the question is out, silence looks like concealment and a vague reply looks like a lie, so the person must either disclose or perform. How you ask decides whether an exit exists. A question with a door in it draws more honest answers than one without.

Offer the exit as you ask: say you are curious, and that they are free to tell you to mind your own business. Then treat a short answer as a complete one and move on.