Boxyboy is the twin of Boxman. He is rarely seen in the game as he is only seen in the cutscenes. In Boxman: Origins, you get a chance to play him in the final level but he would barely move since he is a very frightened boxboy.
It is known that The Idiot has bullied Boxyboy but that have been a drastic guess.
Since he escaped with Boxman out of the drawings to the wild and technoligical future, he have been making friends lately. His first latest friend is Dill Jr. and Kirby. Before then, while in the drawings, Boxyboy had one known friend called Gilbert who was only a few years older.
See Boxman for searches of family