Phil is right...time is very, very short. I had a 500 t/r abrasion strip exit on my aircraft while I was on a 150' line many years ago on a steep slope....in a millisecond the t/r gearbox exited also while in a hover at a high power setting.....the violent yaw of course forced the throttle being closed and dumping the collective...never once did jettisoning the line enter the equation.
Upon contact with the sloping ground, the long line became taut enough to prevent the aircraft from rolling or sliding down the hill....I think it saved my ass when I look back on it....!!!??!!