
John G. answered 09/26/19
Flexible tutor with MA in Classics
The actual answer is, well, neither. They engage with it, in much the same way that an ancient Greek play on the death of Agamemnon would be engaging with Homer's Iliad and Odyssey. The original work still exists, and still stands on its own merits. The adaptation can never truly stand on its own, no matter how closely aligned with the original story it is - or how much it changes to fit the new medium.
While your question refers to "classic" novels, I'm going to use two fairly recent stories that have been adapted: Harry Potter and Percy Jackson. Harry Potter traditionally falls under a "good" adaptation: it tells the same story, changes a few things along the way due to the difference in medium, and scatters references throughout the movies to things that the books included, but the movies were unable to adapt fully. Percy Jackson, on the other hand, lies on the other extreme, where the screenwriters simply took the broad premise and wrote their own movie, with almost no reference to the original text.
In neither case have the original books been affected in any way by the existence of their movies; the movies, rather, do not stand on their own, but consistently engage with the book in respect to the audience - and in both cases, how well they engage with them goes a long way in determining how well they are perceived. So, to answer your question, the books are not affected by the movie at all (albeit perhaps a movie may prompt sales, but that's it); in fact, it is the other way around.