I was speaking with someone recently about things I was reading about mortality salience might lead to a decrease in empathy, and he mentioned that some Buddhist monks meditate on the inescapable reality of their eventual death as a means to build, not hinder, empathy. Unfortunately, he didn’t know much more than that he had heard that.
It’s pretty standard Buddhist practice. The idea behind a lot of meditation is an attempt to gain the other person’s perspective, which is of course what empathy ultimately is. One of the simplest ways to do that is to focus on shared attributes. All people feel hunger for example, so by overlaying your own feelings of hunger onto the hunger of others you develop empathy with them.
Mediating on one’s own death is no different. All humans ultimately share death, and we all fear death. The difference between death and feelings such as hunger is that most people refuse to face their own death, they shut it out. By mediating on the reality of your own death you can more easily understand the effect it has on on your feelings and behaviour, and from their you can understand the effect it has on other people. You also gain an understanding of one of the deepest experiences that you share with other people, that of mortality and the awareness of that mortality.
You appear to have confused empathy and sympathy. They are not the same thing.