I'm not so sure about that, the makers of the game and the DB questline just didn't fleash out the idea very well. With all that goes on in TES I could envision an entity like Sithis devouring the souls of the murdered.
Unfortuantly it's bull. The Dark Brotherhood is an offshoot from the Morag Tong, which with aid of Mephala created a philosophy based on a merger of the Altmer concept of Sithis, limitation, mortality and the Daedric principle of action. As a result, they see murder as the highest act because they actively cause death.
The Dark Brotherhood became isolated from it's original philosophy when the Morag Tong was outlawed and the philosophy of Sithis degenerated from the Aldmer concept into a god of it's own.
As such there never was a god Sithis. This is also most apperent in the varriety of descriptions that the Dark Brotherhood members give of Sithis and it shows that Sithis has never shown himself.