I wonder if the original poster is asking if there was ever a successful attempt to systematically purge an author’s work(s), i.e. book-burning in the sense of deliberately removing an idea from public discourse, rather than, say, accidentally as during the fire at the library of Alexandria?
I had a professor in college who advanced the theory this might have happened to Gaius Cornelius Gallus (70-27 B.C.E?), a poet widely regarded as one of the greats in ancient Rome. He ran afoul of Augustus while he acted as govenor of Egypt after the defeat of Antony–Augustus exiled him and he quickly committed suicide. Despite his reputation (He’s frequently mentioned in glowing terms by other surviving writers, and Vergil made him the apparent subject of his tenth Eclogue), he is not mentioned in Quintillian’s list of “books that should be read” (I.O. book X) written less than 100 years after his death, and nothing of his writing survives (except a chance fragment of papyrus found in an Egyptian tomb, containing four lines).
I disagreed with his view: Ovid was also exiled by Augustus, and lots of his writing survives. I also tend to believe that such attempts to suppress an author’s work always backfire, but must admit I don’t have historical cites to back that up.