"The Mask", After Kathy had killed Ipkiss she decided to take The Mask to Kellaway for safe keeping.
Believing she was not of sound mind Kellaway tried the mask on as a joke and became Big Head. Kellaway as Bighead decided to try to take down all of the big crime lords that had made his career, shall we say, difficult.
After a while Big Heads methods got rather brutal and thus Walter, a giant of a man took a vendetta out against Big Head for killing his former employers.
Because of all the "shenanigans" and "going on's" the police start a hunt for the green headed killer, during the inevitable fight between Big Head and the police Kellaway almost kills his partner. Realising what He did he fled the scene and buried The Mask in cement in his basement.
In "The Mask Returns" Kellaway is the target of the crime lords he previously hassled, he makes his way to the basement but is shot and put into a coma.
Kellaway comes back in "The Mask Strikes Back" and manages to find the four teenagers who are taking turns being Big Head he then tracks down Hugo and Walter but loses the mask after Walter get's frustrated and throws The Mask into the distance.