When someone's heart goes out to someone else, it means they feel sympathy or empathy for that person. Some synonyms for this expression include feeling for, commiserating with, empathizing with, and sympathizing with. Other similar phrases include having compassion for, being supportive of, and showing concern for. These expressions all convey a sense of emotional connection and understanding between two individuals. When someone's heart goes out to another person, it's a sign of kindness, generosity, and a willingness to listen and help. It's important to have these types of connections with others, especially during times of difficulty or hardship.