5

Say there are no cards in someone's library. Can they shuffle their graveyard and hand into their library with an effect that instructs them to do so, if there is technically no library to shuffle into?

8

Yes, you can still shuffle your library like normal even if it is empty. This includes both effects that shuffle your library normally, such as Entomb, and effects that shuffle your graveyard or hand into your library, such as Clear the Mind.

701.19e If an effect causes a player to shuffle a library containing zero or one cards, abilities that trigger when a library is shuffled will still trigger.

So there is no difference between shuffling an empty library or a non-empty library as far as game rules are concerned.

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6

The library is a zone that can contain cards. An empty library is still a library, and an empty graveyard is still a graveyard - a zone still exist even when there are no cards in it.

There was a time where this exact scenario would happen, though mill wasn't very common at the time there were powerful mill cards that people did play, around the time of M11 when cards like Traumatize, Keening Stone with their powerful mill effects, particularly when combined, and when Emrakul, the Aeons Torn, Kozilek, Butcher of Truth and Ulamog, the Infinite Gyre were all in standard.

Milling out one of these big Eldrazi when Keening Stone was taking out the bottom half of the library would lead to the library being empty before everything was to be shuffled back in.

You can:

  1. Shuffle your graveyard into your library when your library is empty.
  2. Shuffle your graveyard into your library when your graveyard is empty.
  3. Shuffle your hand into your library when your hand is empty. (like Time Reversal)
  4. Search and shuffle your library when the library is empty.

We can see this from the comprehensive rules section on shuffling:

701.19c If an effect would cause a player to shuffle one or more specific objects into a library, that library is shuffled even if none of those objects are in the zone they’re expected to be in or an effect causes all of those objects to be moved to another zone or remain in their current zone.

701.19d If an effect would cause a player to shuffle a set of objects into a library, that library is shuffled even if there are no objects in that set.

701.19e If an effect causes a player to shuffle a library containing zero or one cards, abilities that trigger when a library is shuffled will still trigger.

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