Spectra and Dyneema are very low stretch Less than 1% stretch at 20% of break strength. Since most of us use ropes that are way overkill they remain at less than 1% at the loads utilized. They should not bounce back hardly at all. Nylon or any rope that stretches will bounce back...

Dyneema/Spectra is the the way to go as long as there is a good weight on the end.
The comments about it being low stretch is correct i have seen a dyneema rope pulled to its breaking strain on a test bed and cut, it basically just fell on the floor, but the same cant be said for the covers that usually are on the outside of the line, they will recoil when broken under load, for that reason i know several operators that dont run a cover on there lines.

As for the comments on chain snapping, i dont agree if the chain is tested and inspected it won't happen on a helicopter(provided the correct size chain is being used) you will pull the helicopter in half before it would"snap".
The accident being referred to if its the same one im thinking of was a empty chain getting flicked or whipped into the blades.
I have used wire rope and chain along with synthetic and by far the easiest to use is the synthetic.
A bit thread creep i know

I dont use covers because the primary reason synthetic ropes fail is internal abbrasion. They need to be inspected daily. I dont know anyone who actually takes a cover off and inspects the rope every day. That would be a 20 minute process. For me its 2-3 minutes.

The only Dyneema rope I've ever seen brake was covered at all times. Broke at the splice.