The bookstore quest for Alice in Ticker Square is impossible to complete.
She mentions there are some beetles downstairs for you to fight, though there aren't any enemies down there.
Once you get down there all you can do is search for a book. Once you find the book you still cannot complete the quest.
There appear to be three variations to the Alice's Bookstore Quest.
One is dealing with spellbooks.
One is dealing with beetles.
Both of these variations can be completed.
The variation that is finding her missing book, cannot. Acquiring the book does not seem to trigger quest completion in the journal and therefore no turn-in dialogue will appear when speaking to Alice after finding her missing book.
Can close the quest, but she doesn't take the book.
And a DING might be nice when you find the book.