If Consulate Crackdown leaves the battlefield before its triggered ability resolves, no artifacts will be exiled.

Auras attached to the exiled artifacts will be put into their owners' graveyards. Any counters on the exiled artifacts will cease to exist.

If an artifact token is exiled, it ceases to exist. It won't be returned to the battlefield.

The exiled cards return to the battlefield immediately after Consulate Crackdown leaves the battlefield. Nothing happens between the two events, including state-based actions. If Consulate Crackdown exiles multiple artifacts, those cards all return to the battlefield at the same time.

In a multiplayer game, if Consulate Crackdown's owner leaves the game, the exiled cards will return to the battlefield. Because the one-shot effect that returns the cards isn't an ability that goes on the stack, it won't cease to exist along with the leaving player's spells and abilities on the stack.

There are many important moments in the story, but the most crucial—called "story spotlights"—are shown on cards. You can read more about these events in the official Magic fiction at http://www.mtgstory.com.