There’s the tension and then there’s compression. The unobtanium needed to withstand tension forces on a space elevator is one thing. But you need eka-unobtanium to withstand the compression forces on a ring moving slower than orbital speed.
Maybe an unobtainium-adamantium alloy?
No, that’s a bad idea. Adamantium causes cancer.
But of course!
It has to be obvious that Fist of God happened after the downfall of the original Ringword civilization, because the asteroid-destroying system (lased solar flares) would have (should have!) destroyed the whatever-it-was before it hit the ring. As noted, the entire Ring solar system had no other planetary bodies. They were removed either for the raw material, or to make sure nothing could hit the ring.
It isn’t clear if the FoG impact was after the City Builders started stealing the attitude motors. If it was, then the Ring should have hit the star centuries ago. If it was before, then maybe the stabilizing system was still operational. If the FoG was recent (because one could assume the same impact that made it made the leak that caused the Eye storm. Even something as big as Ringworld can’t sustain a leak forever.) then that should bhave been mentioned as the cause of the instability. I think Niven was so taken my the MIT engineers that he forgot his own story. Sure, they told him, a solar flare could make it unstable. And he ran with that. But so, too, would a rock the size of the moon hitting it!
But it definitely wasn’t working when Hot Needle slammed into the ring at some very high rate of speed. The ship left a trail hundreds (thousands?) of miles long and removed top soil down to the scrith. That kind of impact would have moved the ring (and probably killed a million people. Another thing unmentioned.)
One could assume that the FoG was an attack, not a random bit of space debris. But if so, what was the result? One argument against the Pak building the thing was this particular vulnerability. But if they did, maybe FoG was the inciting incident that removed the Protectors and ushered in the era of the City Builders. That would make a good book. too bad we’ll never get it.