A creature with 0 toughness is put into its owner’s graveyard. This state-based action isn’t a consequence of damage, so Zilortha doesn’t affect it.

Because damage remains marked on a creature until the damage is removed as the turn ends, nonlethal damage dealt to a creature you control may become lethal if Zilortha enters or leaves the battlefield during that turn.

Any time the game is checking whether damage is lethal or if a creature should be destroyed for having lethal damage marked on it, use the power of your creatures rather than their toughness to check the damage against. This includes being assigned trample damage, damage from Flame Spill, and so on.

A creature with 0 power isn’t destroyed unless it has at least 1 damage marked on it.