Well, lets not call it exactly "Infinity Mode" but, "exploration mode". The mode would have clear exits, but attaining them would be hard or nearly impossible. Player must FIND them though. It is not as simple as pay off debt. That simply gives you more wiggle room within the mafia.
Now Evil curse? Sounds good, but don't just make it "Evil". What happens if your trapped in Mafia and you try to rob "Good Cult"?
But you are right as to Infinity being boring after a while. Or, it becomes a nightmare. T.O.M.E. infinite Dungeon has true infinite. Including Infinite POWER creep.