Answer

If a player needs to draw cards during the End of the Turn phase to refill their hand, but their deck does not contain enough cards, the following rules apply:

• At the beginning of your turn, if you have no cards left in your deck, you must choose one of your Sanctuaries to be destroyed automatically (page 17).
• The rulebook does not specify what happens if you run out of cards while drawing during the End of the Turn phase (i.e., not at the beginning of your turn).

Reasoning

• The only rule about running out of cards is on page 17: "At the beginning of your turn, if you have no cards left in your deck, you must choose one of your Sanctuaries to be destroyed automatically."
• The End of the Turn phase (page 26) instructs you to "Draw cards from your deck until you reach your hand size," but does not specify what to do if the deck is empty or insufficient.
• There is no mention of Sanctuary destruction or any other penalty for running out of cards during the End of the Turn phase.

Summary

I don't know based on the rulebook. The rulebook only specifies automatic Sanctuary destruction if your deck is empty at the beginning of your turn, not during the End of the Turn phase. It does not clarify what to do if you cannot fully refill your hand at the end of your turn due to an empty deck. Additional clarification from the rulebook or an official FAQ would be needed to answer this situation fully.

Source: page 17, page 26.

Source: Core Rulebook (pp. 17, 18, 20, 22, 26)