If quarry stops because it reached bedrock, and the bedrock is removed by for example a player in creative mode, or a world editing plugin, it will continue to remove all the other bedrock.
The bypass feature of worldguard won't affect NeXTQuarry when the owner of the quarry is offline. (Can't check permissions of offline players)
Mobs which spawn inside, or walk into the quarry, can't be killed manually. (Entity removal plugins such as worldedit or clearlag work though)
