Alex,
If the previous owner bought the books from the Kindle store, they would have been deleted from your Kindle when he de-registered it. In that case, you will have lost the books.
The fact that the books are still present suggests that they were bought from other sources - or that they were free downloads. In that case, the books will stay on the Kindle until you explicitly delete them. Whether or not you are the legal owner depends on what you negotiated with the previous owner (and whether that person had the right to sell them to you).
If the books were from the Kindle store, and they are still present on the Kindle, it might be because you have Whispernet switched off. If so, as soon as you switch it on, I would expect the books to be deleted.
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