I think empathy is the one requirement to care about anyone else's emotions. This is a big problem in my relationship I realized my abusvive partner (which feels nothing like a partner most of the time) lacks empathy, therefore has no care for my feelings.
Every human being goes thru emotions and can usually feel for another if they have empathy. Even animals go thru fear, anger and parental love that is similiar to a human I just learned that in one of my classes. It's interesting that abusive people seem to lack the one the one important element that draws most people together.

I think it's more circumstantial than anything else. I've responded both ways, meaning reaching out to someone who is emotionally distraught and at other times allowing the person their privacy and their space. I'm more than happy to ask if I can help but there are certain circumstances when to do so would be dangerous or not respectful. I allow the person the opportunity to reah out and if they choose not to then I respect their choice.

That was supposed to read...the opportunity to reach out.

I firmly believe that the psyche is form in the early years and our responses will vary according to how traumatic the experience was. What is acceptable to one generation, may be abhorred in another generation. But just for a general discussion I will use your illness example.

For some, hearing of anothers illness or misfortune
Inspires compassion and possibly a beneficent action .

This was me in my early years and early in my marriage. I loved to nurture and care for people and was very attentative towards them.

For someone else, knowledge of anothers illness sends
them running for the door.

This is me now.

Reasons: In my marriage I was constantly ridiculed for going to the doctor, made fun of for cooking for the sick and shut in. Let to dye alone if a serious flu happened or a surgery.

My X made me hate being sick or around sick people. My mother used being sick as a control tactic to control me and my friends allowed me to take care of them knowing they slept with my husband.

So I think before, my psyche was healthy and empathetic towards someone with and illness. But due to the trauma I experienced in my marriage, with my mother and my former friendships, I do not really care if any or all of them get sick anymore. I do not go out of my way anymore. Not that I am unempathetic. But it is a triggering event for me.

Those are just my thoughts.

This is a difficult question for me to answer.

I see it from two view points:

From an intellectual perspective I would say that as a naturally empathic person I would be drawn to having compassion for somebody who is hurting or suffering, and if somebody was happy I would share in their joy.

From the perspective of somebody who has been in an abusive relationship, I would be wary of being pulled in by another person's emotions.

For example with my partner who I am seperated from, towards the end just before I separated I started to take the attitude of becoming completely cold to all the emotions.

Now I can again be more sympathetic and feel that I can listen to my (ex) partner in an open way, yet I am hypervigilent in maintaining some level of detachment in order to prevent the possibility of being sucked in.

In new relationships I also have a tendency to be more aware of both my own behavior and the other person's behavior.