But I thought the whole point of an elevator is you elevate things. Which means the line falling wouldn't be the biggest problem- that would be the payload falling to earth surely?
Spread out over some drop area that's still just a nuisance. Even falling on one area chances of loss of life are minimal, since due to the gradient of gravity accelerating the top end of the wire the least. It should experience way too much drag to have some sort of whip effect on the ground rather than entering a stable configuration before arrival. You'll see it more-or-less neatly arriving in the right order. The first few grams of material landing on your house is maybe a good warning to get out of the way before the remaining 20 tons are done arriving in a few days.
If you have some thin wire design you could also consider just spooling it up as it drops, either at the base or with portable infrastructure you'll have plenty of time to deploy. If you do that you're just dealing with grams of material/second that you can deal with piecewise. Do this faster than terminal velocity and it'll land exactly where you want it to.
That part is not exactly an engineering challenge if you consider what other other stuff humanity likes to get up to with kilometers of much heavier cables and chains.
There shouldn't be much of an issue with designing the the payload as an entry vehicle. Give it the ability to destructively remove itself from the tether, then parachute down. Or just build your tether next to a body of water and have the payload steer into that.
That is if your payload wasn't so high up, it's now on its way to an orbit around earth. I think physically the place of departure should be the periapsis of its orbit, so even with orbital decay through atmospheric drag you'll have long enough to figure where to steer it.
