In the gameplay demo, we saw a Hunter get killed by Rixis Archon Slayer and then revived by his Warlock friend. This tells us that there won't be a 'get to a safe place so your friend can respawn' anymore. You will have to wait until your friends finish pumping lead into aliens. But I think that is only for co-op times. In competitive multiplayer, there will probably be a respawn system but we don't yet know about death when you play by yourself.