In the US, you (and transitively your insurance) are liable as a driver if you cause damage. You can separately have a contract assigning that liability (e.g., the $20/day or so a rental company will often offer to waive basically all physical damage to the car at a $0 deductible). I assume it's that latter sort of thing you're referring to?

I'm not sure how they handle cars damaged under those sorts of policies. I do know those policies are also wildly profitable (I've never come close to approaching eqv. $7300/yr for insurance, despite a horrible driving record when I was younger). Rental cars don't even crash 1.5x as often per mile, so a 5-20x multiple on your premium is noteworthy.