Artists wanting their work destroyed: can they?

Commonly, one of the criteria to judge a great book is its longevity. A book that is read by many, studied by students or scholars, republished by publishing companies, decades after its authors died, is, with little doubt, a great piece of literature.
Yet, some authors expressed the wish that their works – published and unpublished novel, plays, poetry, as well as notebook or library – should be burnt, after their death: Franz Kafka, for instance, or classic author Virgil.
Why did they want their work destroyed? Is it only personal or psychological reasons? Or is there a literary standpoint behind these wishes? If so, which one?
On the other hand, how can we understand their family, friends, publisher “betrayal”? How did they explain it?

Are there, today, artists who expressed similar wishes? Is their explanation different from other past writers? Are their wishes likely to be respected – on a legal level, but also considering the impact the internet and social media could have on the matter?

Or, more, generally speaking, once a book (or film, or TV show…) is released, does it still belong solely to the author, or does it automatically become part of a larger community, which also has some right of inspection?