Dreaming of family accidents is because you are in poor physical or emotional condition during sleep, which leads to inner fear and anxiety. Who are you worried about? I was dreaming myself, so I turned to worry about my family.
Another possibility is that you are dreaming about your family, but when you are sleeping, a sudden loud noise wakes you up, and people are often scared by the sudden sound and have fear. In this way, your dream is changed by this "fear": "family+fear". So you dreamed that something happened to your family.