I love the prospect :D

If cable holds you have gravity, if it fails you risk being slingshot into deep space

The usual design for these things have very low surface speeds, so you're not likely to go off into the deep even if it fails, as you're going to be pretty close to your prior combined orbit even without thrust, and the Δv needed to get back will be tiny.

But also, the forces are never more than the apparent gravity times the mass, so when someone does finally end up experiencing this, it will be part of a larger pattern of bad maintenance and/or engineering that likely has other things going wrong at the same time.

I was only joking, there is no way this would be singular cable without a fallback safety.

Neal Stephenson suggested having two habitats with hooks so they’d spin against each-other. Then you could have fun and climb up to see your neighbors.