I can certainly understand Titlyred's perspective because when INFJ is under extreme stress, they're looking for sympathy. Not necessary empathy. It turns internally in "me, me, me" loop. Not to mention that we also tend to be "negatively" hyper-sensitive and very easily to misinterpret one's intention based on their choice of words.
So I can see why PB's friend might have gotten misinterpreted as she might have wanted a more direct approach as clearly she knew that she hadn't been at her best to remain professional in meetings.
Actually, when INFJs is in stress mode, they suffer a lot as on one hand they're perfectionist to their work, on the other hand they ended up giving up and sabotaging their work ethics. So any questions that might have interpreted toward her professionalism might further upset her. And of course, that's not PB's intention but it's just bad timing.
That is why the direct approach is the best. I can truly sympathize PB's situation as I know NFP has a natural tendency to care and try their best to NOT hurt others' feelings by "rephrasing" their questions into something else that may seem more appropriate for the other. I think PB is trying to be honest but yet she's also careful about not to cross her friend's boundary by phrasing it casually. I've seen many misunderstanding stem from different interpretation of wordings in these situations.
Though I must applaud PB's attempt to drill a deeper understand of how INFJ functions by sharing this story, and asking explicit questions in order to know how to deal with us. I hope I'll meet an INFP like PB soon later in my life.
I think given PB's scenario with her friend, sincerity is the best approach. Perhaps an open invitation for asking her out for coffee (out of the office building), and then say along the lines like, "You seem to have a lot of things going in you, are you okay?" And I'm sure her friend will pour out every little things she would like to share with you. Since when INFJ is highly stressed or depressed, they really need someone to be able to listen to them.Also I think we're pretty good at initiating conversation when we want conversation. That could just be me, and I'd be interested from other INFJs if they feel they are fine with asking for a talk when they want one, or just talking when they need to.
So the key is to display a genuine interest in checking to see if they're okay, by letting them know that you have all the time to listen to their hardships.
I'm sorry if I'm making INFJs sounding more difficult than the description of MBTI, though please remember that when INFJ is suffering from any emotional mishaps, especially to people who are closest and dearest to them, it's often the most painful experience for us to get through as we lack of Fi to keep it all internally to ourselves.
I hope whatever I've said makes sense to NFPs.