I think it would be necessary for a player whose character has died to no longer participate in the RP.  I'd thought about having some sort of second chance clause, like letting them create another character, but I think doing that would be counterproductive.  If there's no penalty for dying, then there would be no real impetus to keep themself alive, other than a sense of attachment to their character I guess.  

The way I had it in my head is that the RP would be almost completely based on character development and interaction.  Would a player want to try to form bonds and create allies, be a loner, or an opportunist who would throw another character under the bus to live through the round?  Trust, guile and suspicion would all be equally important.