Has a famous, yet reclusive author ever died, and then, rather than telling the public of his passing, the publisher continued producing books in his name using ghost writers?

This doesn't quite fit your criteria, as Andrews wasn't reclusive and her death wasn't a secret, but the last 68 out of 75 V.C. Andrews novels have in fact been written after her death by a man named Andrew Neiderman. He was hired by the publisher to finish a prequel to Flowers in the Attic from Andrews' notes, and they kept him on to ghostwrite after its commercial success. Buzzfeed (really!) has a good article on the subject: http://www.buzzfeed.com/kateaurthur/the-ghost-of-vc-andrews-the-life-death-and-afterlife-of-the#2eg56vb As the author of that piece notes, Andrews' death wasn't secret -- her obit was published -- but since it was before the Internet, it would have been easy for her fans to miss the announcement and keep buying the books.

Neiderman has been ghostwriting the novels of V.C. Andrews since shortly after she died from breast cancer in December 1986. And though Andrews’ death was not a secret (all the major newspapers carried her obituary), in a pre-internet age, it was easy enough to continue publishing books under her name so prolifically that the news of her death might have faded from your memory — if you had happened to hear of it at all. Keeping her alive — even if just in spirit — was simply smart business.

The article also notes that other "pen names" have been used by a variety of authors, but claims that the Neiderman/Andrews situation is unique in that it is only one author who has continued to ghostwrite under the name, rather than a team.

V.C. Andrews is not the first writer to continue to produce new works after death. Sebastian Faulks wrote Devil May Care, a James Bond book, in 2008, and the cover read, “Sebastian Faulks writing as Ian Fleming.” There’s the case of Robert Ludlum, who died in 2001, but whose name was trademarked for several subsequent ghostwritten novels; there’s Robert B. Parker, who died in 2010, but whose characters live on, written by multiple ghostwriters. And then there are series like Nancy Drew, which are entirely written by collections of writers-for-hire under one pen name. But the Neiderman-as-Andrews arrangement is different in that 27 years after embarking on writing his first V.C. Andrews books, he is still the sole ghostwriter writing them.

I could talk more about Clancy and Ludlum, in particular, but they're within the last 20 years, so not history yet. :)