Orbital and escape velocities??? The elevator is sitting over a stationary spot... it's moving at earth's rotational velocity. Only the portion above the GEO anchor is moving at orbital velocity.
But it has altitude. The stuff that's low down doesn't have a lot of orbital velocity, blow the cable and it falls nearby. And the stuff far away has enough velocity that it goes into a very eccentric orbit rather than hitting the atmosphere.
Just because it's moving below circular orbital speed doesn't mean the periapsis is in the atmosphere.
Just because it's moving below circular orbital speed doesn't mean the periapsis is in the atmosphere.