I think all of this depends on the UI presentation, but when “shuffle” is used, I think a good starting point is “what would a person expect from a deck of cards”, since that’s where the metaphor started.

I don’t think that provides a totally clear answer to “what happens at the end”, but for me it’d lean me towards “a new shuffle”, because for me most of the time a shuffled deck of cards draws its last card, the deck will be shuffled again before drawing new cards.