Just beat it, thanks to Ancano spending all his mana fireballing my unconscious Lydia. Somehow she survived. I'm just curious, is it possible for companions to die while paralyzed?

Only if you deal the last damage, or they are attacked while they are "dazed." She must have bugged if he was continually pounding her.

Enemies will stop attacking them if they're downed, but if you're fighting casters or the like then they can hit the companion accidentally while aiming through them at you; that's how my Lydia died.

the strategy guide tells you that you either have to deal the final blow yourself or they have to take poison damage that is more powerful than their health regeneration upon falling to one knee. So far that hasn't happened to me and I have never lost a companion permanently.