A recently unearthed play by Horton Foote has been hauled out of a desk drawer and thrust onto a New York stage this summer for its first “major commercial production.” But unlike many unpublished works by well-known playwrights, which tend to be underdeveloped and youthfully insecure, Foote’s work, which received its premiere at Whittier College in 2000, is a mature play, written when the author had already achieved a great deal of critical acclaim. “The reason it has not been staged before has more to do with his gentlemanly sense of propriety than any reluctance by a producer to stage it.”