There isn’t a lot of research that explores the connection between empathy and recovery from trauma. However, the connection between social support and the development of Post Traumatic Stress Disorder after a traumatic event is well documented. Trauma survivors who have lots of social support after a traumatic event have less posttraumatic stress symptoms than those with a lack of support, even if they experienced more severe trauma. The type and level of social support isn’t usually explored, but presumably at least some part of it involves receiving compassion and empathy from one’s supports. Also, people with fewer social supports tend to have more severe symptoms of posttraumatic stress. It’s not clear whether having less support leads to worse symptoms or the disruptive symptoms of PTSD lead to less support, but it’s clear that they’re related.
Above are illustrations of three types of empathy from Daniel Goleman and Paul Ekman