A remote, desolate, and depressing place much like the "friend zone" into which those good friends named Ben (or any articulation of the name) are cast by a prospective mate. There is a subtle difference however, unlike the "friend zone," where the attraction is solely one-sided, those in the Ben Zone have been cast there by one who reciprocates the attraction, but has deemed any progression beyond friendship to be illogical, which in and of itself is illogical.
Girl: Ben, I like you...a lot, but I think we should just be friends.
Ben: Oh, ok then...
Ben's Friends: Ben, we're so sorry, you're in the Ben Zone.