The Closet is where The Boy hangs up his clothes and is cluttered with messy dirty clothes lying around (which is probably how the Closet Monster was created). The Closet is also used as storage for many of the Boy's belongings such as a baseball bat and a bowling ball.
Mr. Bumpy has sometimes come too close to the closet, especially when the Closet Monster lures him with a dirty sock. The Closet Monster then tries to capture Bumpy and eat him, or attacks him for getting too close to his lair.
Other characters avoid going into the Closet because they fear the vicious Closet Monster. In the episode "To Sleep Perchance to Burp" Molly Coddle warns Mr Bumpy that "So many toys have gone into that closet never come out". In the episode "Comforting the Uncomfortable" Molly goes into the Closet so she can attempt to comfort the Closet Monster and to befriend him. Sometimes when the Closet Monster escapes and goes on a rampage, they often defeat the Monster by trapping him back inside the Closet.