Is the driver obligated to do anything towards a person who claims injury from his car, though he is not sure of the harm, while also fearing that the injured person might be a danger to his family?

Rights are not established as obligations unless one knows or has a strong presumption of their necessity, and the default is the freedom from obligation. If the person is unknown and cannot be reached, then one should seek Allah's forgiveness, increase good deeds, and supplicate to Allah to bear the rights of His servants on the Day of Resurrection.