I once worked with a manager who would always ask for details like "oh you have a headache? Do you have a fever?" While I think his intentions were good, and that he just wanted to show concern and even offer support or advice, I always found the questions incredibly invasive and a violation of my privacy.
My team knows that I will always listen if an employee wants to share details of their personal lives (upto anything that crosses the line of appropriatness for work), but I would never pry.
So, in this example, I would never know an employee is struggling with a personal issue, unless they broached the subject with me.