Variation on the concept. Space elevator is tethered at both ends; this thing forgoes the Earth-bound tether and hopes the hanging end stays within a very narrow tolerance range (lest it start smashing things up at high speed).
If you can keep it from swinging into mountains it might make a better space elevator than the Clarke. It can be supplied by helicopter and tons of stuff can be orbited on the cheap.
“Hope” is the key word there. The variable wind shear forces at different altitudes affecting the structure would probably tear the thing pretty quickly. If not, the hanging structure is basically going to act as an anchor pulling the asteroid towards the earth.