Since ya'll downvote without bothering to cite, why don't you try reading:
In fact, given that we're hand-waving the strength problem away - you'd be dumb to have a space elevator at all, since that requires power to climb it. When instead you could go to orbit for free. See the rotating options on that wikipedia page.
Don't tether it to the Earth. Drop it down so it's reachable by planes, then you've got a lot fewer problems if something hits it/severs it; everything above the sever doesn't become a potential kinetic impactor, and if you've put rockets along the length up, you can fire them and take the rest away as well.
If you place it in the ocean, and when it drops you'll take out coasts on both shores.
Added bonus, since its terminal end is not anchored, you can move it around if the country / ocean you're above becomes problematic, or doesn't want to pay you enough / trade demands - you go somewhere else.
If you have problems anywhere along the length of your elevator, it's going to lose its balance, and become a nice falling object.
As long as the damage happens to the half which is below the equilibrium point, the remainder of the portion above the severance point will fly off into space (ie: not becoming an impactor).
If you've secured one end to the planet, any damage above that point has to become an impactor (ie: up to 99.9% of your elevator) unless you have coping mechanisms.
The simplest coping mechanism is to quickly spool up anything that's not severed, or to rapidly put a larger weight further out. You can also joist anything below the equilibrium point up with rockets, assuming you cut the tether at the ground level - otherwise you're merely putting off impact until your rockets run out of fuel.
If you're tethered to the Earth, then you have a pretty hard limit on how much remaining elevator length you have. If you lose it right at the equilibrium point, you will need a rocket which can lift the whole remaining mass up out of the gravity well (expensive), as well as being able to release it from the ground.
If it's not tethered to the ground, you have a lot more options for anything that's not severed from your structure (ie: the only risk is up to half of the elevator below the equilibrium point (which is also shorter since it doesn't reach all the way to the ground). You also have more time to react, since you've got 10K feet (for example) before impact starts to occur.
The simplest way to do this, is to have a landing bay/pad at the lowest end of the non-tethered elevator, and if anything happens, sever that weight (which is lowest, and probably weighs less than your at-risk portion of the elevator). Yes, you drop something from 10K feet, big splash. You don't lose the rest of your elevator. In this example, the tether/ribbon/elevator is longer, or has a counterweight past the equilibrium point to balance the weight of your landing bay.
Or, to be more clear:
How does cutting the bottom 5-30 km from a 36000+km ribbon prevent it from becoming a kinetic impactor?
It prevents 35,940+ km worth of ribbon from being an impactor, which if the top 30km of your tethered ribbon got severed by terrorist, space junk, micrometeorite, etc would (most likely) be the case.