Well, first... I never really understood... is this PBF section of the message board strictly for PBF games, or also for all PBF related discussions?
It's for all things PBF. Discussion included.
As for the question... If players get eliminated through the trial/boxing mechanic in Exodus' Ionian Nebula option, then technically, they're done. Are they then free to join a new BSG PBF game at that point?
They are no longer playing, so I would say yes. The point of the list is to be fair to those not yet playing. If their game is over (and for them it is over early), they should be back on the list, or if back on the list and up front, free to play right away. No need to further punish that player.