Any person who legally kills any big game and discovers that the flesh of the big game was unfit for human consumption at the time of killing shall, within 12 hours following the discovery, deliver the entire carcass, less entrails, but including the head and hide, to any commission officer who, being satisfied that the big game was unfit for human consumption at the time killed, shall issue a written authorization to the person to kill a second animal or bird of the same species during the unexpired portion of the season for that species.