Suppose there's a problem somewhere around L1. If there's a space station, it cuts its losses likely starting with the counterweight, dominated by rope. The elastic cables fall. Let's look at Sinus Medii's side first.
Up to 60 Mm of Kevlar or Dyneema collapses upon the base. Coil it, box it, unscroll it - what is the base supposed to do with all this?
At the highest apogee, is potential-energy. That's the integral mg(h)dh. Prepare for terajoules. The drop of this cable is a force, perhaps accelerating as more falls; like a slow motion explosion, more Chernobyl than Nagasaki. Loonies can harness this, but maybe not by design.
Under that; I want some structure as can funnel the thousands of m3 to some convenient depository away from useful work. We need to place it somehow/-where so we don't knot it and doesn't get METEORED. The depo would be large and/or deep: a fair purpose for a kilotower. Assume the depo is dustfree anyway. (If we're banning lander-rockets, that should help.)
