If the deck runs out, the deck simply ceases to be an option for players to draw from or interact with. Therefore, if a player must reveal or draw a card from the deck as part of an effect and the deck is empty, they cannot perform that part of the effect.

This is stated under "Edge Cases" on page 3:

• "Deck runs out: If there are no cards in the deck, the deck simply ceases to be an option for players to draw from or interact with."

Source: page 3

So, any effect that requires revealing or drawing from the deck cannot be completed if the deck is empty.

Source: Core Rulebook (pp. 1, 3, 4, 6)