Eggy Mule is one of the hired enforcers mentioned during a conversation between Slim Charles & Avon Barksdale in the episode "Homecoming." Avon inquires about enlisting Mr. Mule as muscle in the war against Marlo Stanfield, however, Eggy was previously sentenced to five years in prison after federal agents caught him with a handgun. The name 'Eggy' has been considered farcical by some commentators. As has the surname 'Mūle'.
There is also a reference to "Eggy" during the pilot, when Stringer Bell is having a conversation about activities in the high rises. It's not clear if this reference is to the same character.