[lmkg]

If a string is hung between two fixed points, then it will fall in the shape of a catenary (hyperbolic cosine):

http://en.wikipedia.org/wiki/Catenary

Even when one of the ends is weighted down rather than fixed, I think it's still going to want to fall into a catenary curve, because that curve minimizes the potential energy of the string itself, and there is some equilibrium between the lower potential energy of the string and the higher potential energy of the object. How far the curvature departs from a straight line is probably a function of the ratio of mass between the lifted object and the string itself. With a whale and some yarn, it's going to asymptotically close to a straight line, but still slightly curved. However, fail whales are apparently light enough to be carried by a handful of birds, so the weight is probably comparable to the string itself.