Hmm... We ARE talking imaginary technology here you know?
Still... Main safety concerns should be meteors.
Asteroids are big enough to notice and steer away or destroy in time.
That WOULD be a space faring civilization. Moving a big chunk of rock would be akin to... well... moving a big chink of rock on Earth.
Get some trucks and load it in, or get some explosives and blow it up.
Adjust for the size of the rock and it being in space, not on Earth.
So... only thing they would have to fear would be those really small and yet REALLY tough and really fast meteors small enough so that could stay undetected until it is too late and still powerful enough to do significant damage to the ring.
And I don't know about you, but if I was building a space structure that could be hurt by meteors and flying debris I'd put some automatic detection and point defense systems on it.
Several of them. With backups. And shields.
So, what we have is very thin (compared to Earth) ring structure in a stable orbit (has to be stable - can't anchor it otherwise) made with Magic-techTM that could be compared to a piece of thread around a large beach ball.
Now... try breaking that piece of thread by throwing grains of very fine sand at it.
Naah... ring is quite safe as long as it is maintained.
Now... failsafes...
Anchors are irrelevant as far as the ring is concerned.
WE, the humans, living on the planet need the anchors to get TO the ring and back down. Ring will spin up there just fine even detached. For a while, anyway.
What I am saying is - ring is stabilized from above, not bellow.
Systems for that should of course be autonomous and robust, with multiple levels of backups etc.
Still, once you get something in sync with the Earth and the Moon's gravity well and rotation, it will stay up there for a while.
Stabilization would be needed mostly, again, because of the anchors.
Couple of hundred meters to the left or right might not mean a lot to the ring, but to the anchor...
But, as we see from Tiphares' cables (rather loose) builders have done their job quite well...
Even with things falling apart around Tiphares it has not moved an inch in centuries.
But let us for the sake of the argument say that there is some kind of a major disaster.
Say... some imaginary terrorists sneak a H-Bomb into the elevator and blow it up on the upper end.
So, we end up with a broken ring, spinning out of sync with Earth and ripping itself apart and raining pieces down to the ground.
First off... I'd have that same system that has been syncing the ring to the Earth and the anchors on it for centuries.. well... do its work.
Re-stabilize the remains of the rings.
Detach the sections that unbalance the remaining structure and have them either jettisoned into space (use the stabilizer's thrusters of that section) or into a safe orbit, or if all else is unattainable - have it crash in Tunguska, not over Scrapyard.
Same thing goes for the elevator.
Depending on the which sections of the tube are salvageable have them
a) float into orbit to be reassembled later,
b) parachute to the ground to be reassembled later,
c) burned from the inside out with plasma and/or other magical technology that could easily destroy such a structure from inside but not from outside,
d) leave the couple of hundred meters of the elevator on the bottom as they are.
I mean... come on... just because it can be broken does not mean no one will try to fix it again, right?
For something THAT big to be built someone would have surely thought about all these scenarios and would have planned accordingly.
Now... Tiphares, being detached from the Earth, and essentially just "hanging there" - Scrapyard and Tiphares would be fucked.
Were they still connected to the Earth, they could just follow the d option and have those shields they have shield them from the debris.
But, as they have blown up their bottom - there would be no section to implement the d option on.
But look around you ...
Death and Light are everywhere, always, and they begin, end, strive,
attend, into and upon the Dream of the Nameless that is the world,
burning words within Samsara, perhaps to create a thing of beauty.