The reason why courts and law enforcement officers are put in charge of the justice system is to ensure that punishment is equal to crime committed. There is no single human being who would accept for the death penalty to be executed against a person who has stolen. It would be a miscarriage of justice for a person to be executed for stealing a wallet and this is what the result is.
Different people would apply force on the accused person. Some may not even be witnesses to the incident but will be carried away by reports given by others which may even be exaggerated. The injuries inflicted may result in disability or death. When such deaths occur the mob is charged for breaking the law and the accused person becomes the victim.
It is important that society develops to a level where crime will not be committed to fight crime. The real objective of justice is not only to punish wrong doers but also to rehabilitate them so that they will fit in society and live productive and contributive life after their punishing them.