He is the guardian of the Gate of the Abyss, a dimension even lower than the underworld.
Tartaros himself is unable to leave the gate, so he leaves his activities outside the gate to Koufís.
Titan, a weapon of the old human race, contains the souls of those who were sealed in the gate as well.
He has been in the state of a soul for a long time, and even after he became Koufís, he has forgotten what he was originally like because he is alone in the empty void of Tartaros, the final disposal site of his soul.
He has the mental strength to accept this as one of his sins. Where his strength of consciousness comes from...he himself does not know.