Billy is the ghoulified child of Carol Peabody and Matt Peabody who hid in a fridge to protect himself from the bombs dropped during the Great War. When Billy entered the fridge he became trapped due to its locking mechanism not featuring an interior handle. The fridge, in which Billy has been trapped for two hundred and ten years, is found next to the road in between Neponset Park and University Point. Billy claims that he was playing with his friends before the bombs fell. He also claims that when the sirens went off, he tried to find his way back home to his parents.
Kid in a Fridge: The Sole Survivor can help Billy return home to his unknowing ghoulified parents. During the journey, the Sole Survivor will be approached by a slave dealer named Bullet where they will be given the option to sell Billy into slavery.
If the Sole Survivor kills Bullet after selling Billy, they can restart the quest to take Billy home.
Although not currently explained, ghouls may be able to survive without food, water or air. Billy survived locked in a fridge for 210 years with presumably only what was left in the fridge, similar to how some feral ghouls are locked away for years and how Coffin Willie was buried alive for months. This suggests an ability to survive on radiation alone, despite being shown by Harland in Fallout: New Vegas, as he eats radroaches and drinks pipe condensation to survive, and within Fallout where the entire city of Necropolis will die out if the Vault Dweller take their water purifier's control chip.
In fact, it also contradicts the settlement system in this very game; in the settlement system, generic settlers have a chance of spawning as ghouls, who will require food and water just like regular humans.
While ghoulification is known to halt the aging process in adults, it appears to halt all aging in humans, as Billy has remained a child for 210 years with apparently no further growth since its onset.
Despite being locked in a dark and very confined space for a considerable time, Billy is able to see without hindrance and can do motor functions just fine.
He is also perfectly sane, though it is known that people can be driven insane if they are forced to spend days in cold, cramped, confined spaces.
When you help him and return him to his family it appears that word travels fast. Seeing as Diamond City Radio will mention the Sole Survivor "reuniting him with his family" and Diamond City security will deny believing claims that they were seen with a ghoul kid ("there's no such thing I told him").
If the Sole Survivor gets into a fight with hostile enemies and Billy is near, he will crouch in cover and stay away until there are no more enemies that detect you/him.
Billy is currently the only ghoul child to appear in any of the Fallout games.
The robots at Easy City Downs appear to try and attack Billy when their combat inhibitors have been disabled and targeting parameters overridden. If you leave the location, eventually Billy will rejoin you.