Their starting point obviously isn't above their ending point, though.
mansr is right, I've been looking at this all wrong because I assumed the weight of the strings was small compared to the weight of the whale. But if the strings are dense they will curve under their own weight. So we're not looking at a super-light whale, we're looking a regular whale supported by super-heavy strings.
(Where do you get strings so dense that the mass of a short stretch is comparable to the mass of a whale? Why, the same place you get those goddamn birds, of course.)