I am on the run,
There is no place for me,
I am the victim,
There is no charity.
-- Project Pitchfork, "Hunted"
Renegades are the rebel's rebels. Either because of dissonance or angering the wrong Demon Prince, these demons have crossed the line and gone on the run from Hell itself. A precious few seek something higher and redeem but most simply try to live their lives and keep their heads down.
A Renegade is in a slightly different position from an Outcast. There's nothing stopping a runaway demon from using his Superior's Rites, going back to Hell or even calling his Prince -- but it would be foolish to do so, since the Prince (and the secret police of Asmodeus) undoubtedly wants his head on a stick. On top of that, a Renegade's Heart does NOT automatically crack the way an Outcast's does ... if he wants to keep from being found, he's going to have break that Heart himself.
Unlike an angel, a demon cannot become Renegade simply by failing a dissonance roll; doing so will cause him Discord instead. Obviously, he then cannot fail another dissonance roll to "un-Fall"; the road to becoming an angel again, known as Redemption, is much more difficult than that, involving a personal choice to give up his selfish nature and the intervention of an Archangel.
So-called Free Lilim have an easier time than most in going Renegade, since they have no Hearts to break.
Renegades that have erased all their dissonance aren't quite out of danger yet -- but they may be able to find a Prince (not necessarily their old one!) who will take them in and give them protection. Some Renegade demons even prove so effective on the run that they get an amnesty from Lucifer, and maybe a Word. But most don't especially want to come "home"; either they don't believe it's safe for them, or they've become tired of fighting for the greater glory of Hell.
A PC demon who starts play as a Renegade begins with 3 levels of Discord.