Half of the players at the beginning of the game were immune to assimilation, and others were added to that list as the game went on.

The Borg Queen was able to survive a failed assimilation attempt, but no other Borg were, so if they continued recruiting after her death it was likely that the cult would die out.

There were also several ways for people to get clues about the Borg's presence but only one, from your protecting White Flame, actually happened.