If an Aura's enchanted permanent no longer exists, is the Aura put into the graveyard as a state-based action?

State-based actions are checked continuously, and one of them specifically covers Auras that have become unattached from a legal permanent. Under CR 704.5n, if an Aura is attached to an object or player that it cannot legally enchant—or is attached to nothing at all—it is immediately put into its owner's graveyard.

When a permanent an Aura enchants ceases to exist (e.g., it's destroyed, exiled, or bounced to hand), the Aura is left 'floating' with no legal attachment. The game checks state-based actions and sees the Aura is no longer attached to anything on the battlefield, triggering the rule above. No player receives priority before this happens; it's automatic.

It's worth noting this is distinct from the Aura being destroyed 'along with' the permanent. The enchanted permanent leaves first, and then the Aura is placed into the graveyard as a state-based action. This matters for effects that care about how things die or leave the battlefield.

Example: You control a Grizzly Bears enchanted with Pacifism. Your opponent casts Lightning Bolt, destroying the Bears. Before anyone gets priority again, state-based actions are checked: Pacifism is now attached to nothing, so it is immediately placed into your graveyard per CR 704.5n.