Didn't the mafioso tell Denji that he never liked him, on a fundamental basis, just before the other dude stabbed him in the back? I'd say that would explain sufficiently the reason why Denji was kept living as he did. Basically, the mafioso always hated Denji, and likely had wanted to kill him for a very long time, but as long as he needed to run his little gang, he did put Denji to work as an asset, but most likely he would have been quite happy if some demon had killed Denji. More importantly, he hated Denji for Denji being like he was: a faitful dog who never tried to fight back, never tried to run, was even willing to sell his own organs, accepted without a complaint the absurd reductions in the rewards. The mafioso hated such a man, yet because of it he knew Denji would never run away, so it didn't much matter if there was seemingly no leash. It allowed him to contact Denji whenever he wanted, but he also didn't need to see Denji too often, except for the occasional jobs.