I don't know about specific cases, but I do know that when a "duplicate" production of a show is produced (ie tour or sit-down production), then either the director themself goes to stage it OR an asst director or stage manager will do it. Mostly, according to my experience, it is the director that comes.
If you think about it, all the "directing" is done. The show is blocked and it's all on paper. As is the "acting" although the acting can vary.
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle