Just an idea - do with it as you wish...
How about having the white belt rank kinda like a one way door. Once you step through it, you can't step back. If a fighter on ANY progression manages to fall to the last level of disgrace on the second tier (first true tier of any path), their next fight (where they would fall back to white belt if they lost) is automatically a death match (for them - not necessarily for the other fighter) and if they lose then the other fighter has the OPTION to kill them. I stress option because I don't believe that death should be automatic for anyone. If the fighter chooses not to kill the loser, then they would remain at the same level of disgrace (effectively in the same boat - possible death in their next match.)
This would keep the threat of death real for ALL, not just the villains.
The first real problem I can see with this would be switching paths. It would have to be stated somewhere that you couldn't voluntarily do anyhting that would cause you to lose enough ranks to drop you back into white belt. If you wanted to switch paths, you would have to build yourself up high enough to be able to do it first. Or switch in baby steps - Yakuza to Sash, then eventually to Honored, or vice-versa.
I'm sure there are other problems but I'm not seeing them right now. Anyways, those are my thoughts on the subject.