It is a well known effect (hazard) that when a steel cable breaks under tension, it comes flying back, snaking all over the place. Now, steel stretches very little at failure, so this snaking is due to a transverse wave being induced. I suspect that the same thing can occur in a poly rope.
Tom

I think I can see why steel cable does what it does on breaking and why towrope wouldn't really behave the same. Upon breaking, the stretch of steel cable is released with a lot of acceleration and because of its momentum, it overshoots its neutral length. The cable has rigidity and buckles energetically when it recoils and pushes upon itself throughout its length. By contrast, poly rope has no need of buckling; it can go placid as it arrives at neutral length. Once placid, it won't support wave propagation in transverse or longitudinal mode. So, if there's any waves generated at the first breakage, those waves need to finish their work before the rope finishes unstretching.