I think there should be some king of respawn mechanic because one of the biggest turn-offs of BR's for me is having one of your friends die and then you either have to restart or play on without them. I think as players who drop in the second wave spawn with guns, if one of your teammates dies they should respawn in the second wave without a gun as long as you wipe out the squad that killed your teammates.
I think it's fairly unlikely we'll see any respawn mechanics after an actual elimination. Downs will have the ability to be brought back up like some others.
Rather than the same people cycling into a game which doesn't make much sense. Otherwise it would just become a TDM game mode eventually.