What does Talix's Soaring Ash return to the turn order deck, and what happens if that deck is empty?

Question

Accepted Answer

Talix returns one of his own turn order cards to the turn order deck. He does not reveal from the deck, so if the deck is empty his card becomes a one-card deck and he gets the next turn.

Aeon's End: The New Age

What does Talix's Soaring Ash return to the turn order deck, and what happens if that deck is empty?