To answer this question, we are going to refer to some previous digests:
In practice, this means that if a player has exactly 8 cards in their play deck and they play Eyes of Mandos, they need to take those 8 cards out of their play deck momentarily in order to resolve the card’s text, but doing so doesn't count as “exhausting” the play deck because they are not drawing those cards or putting them into their hand. The same thing would happen if a player plays Great Secrets Buried There against an opponent with exactly 10 cards in their play deck, etc.Clarification: Your play deck is “exhausted” when you draw its last card. Some cards require that your play deck be manipulated and then reshuffled—this does not “exhaust” your play deck. [COE 21]
If you are required to draw cards and your play deck already has zero cards in it, you are not considered to be “exhausting” your play deck (because of the above rule). [COE 82]
If a card is sent to your discard pile when your play deck already contains zero cards, the discarded card immediately becomes your new play deck. If multiple cards are sent to your discard pile while your play deck contains zero cards, those multiple cards are shuffled into your new play deck at the same time. In other words, you can never have a card in your discard pile but not in your play deck. [COE 82]
If your play deck and discard pile contain zero cards, you may still take actions that require you to shuffle a card into your play deck, such as Smoke Rings. [COE 82]
On the other hand, if a player were to play Eyes of Mandos with only one card in their play deck, they would reveal that one card and put it into their hand (per the text of Eyes of Mandos), which would effectively exhaust their play deck. The same thing would happen if they were to play Inner Cunning as a short event and the last card in their deck was Baduila.
Returning to the original question: Since a player is only considered to have ‘exhausted’ their play deck when they draw the last card from it, they would need to draw the last card again to exhaust the play deck again; but if the discard pile had zero cards when the play deck was exhausted the first time, they wouldn’t be able to draw another “last card” because they wouldn’t have any cards to draw.
At that point, they would need to keep playing with whatever cards they already have in their hand and in play, without being able to draw any more cards until one of the following occurs:
A card is sent to their discard pile, at which point that card automatically becomes their new play deck. Note that this is not considered an action that can be responded to, as it resolves immediately.
A card is added to their play deck through some other mechanic (e.g. by playing Smoke Rings).
Once the player has a new play deck, they are considered to have exhausted their play deck again the next time they draw the last card from it, and so on.