I would interpret this to mean that you will give me my pick of any single book that remains available when I am allowed to choose.
If you had said, "I can give you any books that are left." I would expect that I would be given all the remaining books.
Some can be used to indicate indeterminism so if you had said, "I can give you some book that is left." I would expect to receive a book but, possibly not one of my choice.
Some can also be used to mean "not all" so if you had said, "I can give you some of the books that are left." I would expect to receive more than one of the remaining books- And here my expectation would be that I could help choose from the available books.