Generally when I know the Black Death is coming I move all my best characters and most expensive and experienced units outside my cities and have them sit it out until the plague has passed. Once it has gone I immediately go on the offensive, on the grounds that the plague will have damaged my enemy's economy as much as my own, but it will have depleted his troops while mine were safely outside the walls. For some reason armies on the march seem to be immune to catching plague; kind of silly since I believe disease was actually one of the greatest threats to a besieging army.

Quote Originally Posted by Insane834
Is it possible to destroy a faction using the plague, such as killing all of their generals and family members so there is nobody left to be king
I suspect not, I believe the computer will simply adopt new family members to replace the old ones. At least this seems to be what happens when I try to eliminate a (non-horde) faction by assassination; even if I kill all the family members in one turn, the faction survives and next turn has promoted a bunch of captains.