Everyone knows how annoying it can be to have your round ruined by people who are ghosting either intentionally or accidentally. Open Chat is notorious of this. I would like to suggest that each chat (dead, alive) exist in their own channel. Living players can only hear living players. Dead players can hear both themselves, spectators and living people but cannot talk to the living. They can only talk to living players though private message or any other means of communication. It will be like how it works in TTT. I do not know if this is indeed possible. If it is however, I would like to see this added.
See the problem with this is the fact that open chat is part of the fun of a deathrun server. Getting cheered on while being one of the only ones left, getting laughed at by an alive player after your fail at bhoping leading to your death was seen, and bragging to others how you narrowly escaped death when they were just obliterated by a certain trap. I feel that in TTT ghosting would be a huge problem, but in Deathrun, the problem would be minimal. Sure a trap might accidently be revealed (Left,Right,Left), but there are always more traps. TL;DR: The reward outweighs the risk.
As long as ghosting is punished I have no problem with the chats being global, like Average stated, the egging on is some of the most fun in DR.
The biggest + of DR is open chat. If you notice, the ratio of you being dead to you being alive is much higher in DR than TTT, and yet more people alt-tab from TTT while dead while less so in DR. It's really just because you still can do shit while you're dead. You can goad players to do traps, mislead them, or whatever else goes in your twisted mind that doesn't violate the rules. This is TTT's biggest hurdle in my opinion, of which the best solution is !dm, but sadly, as you might have seen, it has been shut down for every time it cropped up.