On the tether there is a "zero" point. Below that point things fall toward the Earth, above that point things "fall" away from the Earth.
So it depends on where it broke and how much weight there is above vs below that point. (To keep the tether in the air they put lots of weight above the point, which falls away from the Earth and pulls the tether taught.)
If I were making one of these I'd make several tethers, spaced such that a single object can not break more than one at once. Then tie the tethers together periodically.
This object is about max: https://en.wikipedia.org/wiki/Tunguska_event so I'd make the multiple tethers at least 200m apart. That's pretty far apart, so I'd invest in better detection technology to reduce the size maximum undetected object. (Although that raises the question of what to do if you do find a big one and it's headed right toward you.)