Billy is the son of Carol Peabody and Matt Peabody who hid in a refrigerator to protect himself from the bombs that were 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 between Neponset Park and University Point. Billy claims that he was playing with his friends before the bombs fell and 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 ghoul 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.
Billy creates a currently unexplained inconsistency in the Fallout world by showing that ghouls may be able to survive without food, water or air. Bullet, to whom Billy can be sold, remarks that ghouls do not need to eat and are immune to aging. 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 or the ability to enter a state of hibernation, as demonstrated by feral ghouls. In contrast, Harland in Fallout: New Vegas explains that he had to eat radroaches and drink pipe condensation to survive, and within Fallout, the entire city of Necropolis will die out if the Vault Dweller takes their water purifier's control chip. This is not even consistent with Fallout 4 since Kent Connolly needs sustenance to survive, which is mentioned in Irma's terminal.
In fact, this also contradicts the settlement system in Fallout 4 itself; in the settlement system, generic settlers have a chance of spawning as ghouls, who will require food and water just like regular humans.
In the same vein, the quest Duty or Dishonor shows that even feral ghouls require food, as Initiate Clarke steals supplies to feed a pack of feral ghouls within the Boston Airport ruins because he believes it is immoral to just kill them, as well as to prevent them from getting hungry and attacking Brotherhood of Steel personnel.
While ghoulification is known to halt the aging process in adults, Billy's existence asserts that it prevents 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 perform 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 just days alone in cold, cramped and confined spaces, including a refrigerator.
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 the player character.
Billy is currently the only ghoul child to appear in any of the Fallout games.
The robots at Easy City Downs will try to attack Billy even when their combat inhibitors have been disabled and targeting parameters overridden. If the Sole Survivor leaves the location, eventually Billy will rejoin them.