They are called "self-supporting" run flats.
If punctured, they can run for about 50 miles (100 on the 'vette tires) at zero pressure.
They achieve this by increasing the sidewall rubber by about 4X, adding weight (about 5-8 lbs PER TIRE over the non-runflat version of same size tire), and resulting in a VERY hard ride.
The harsh ride also highly dependent on the load rating of your tire versus the actual load that your car operates at, coupled with the sidewall height (aspect ratio X section width). Self-supporting run flats work best if the sidewall height is low (<105mm or so).
Example: if you work out that your car SHOULD have a load rating tire of about 88-90, going to a run-flat would work for a tire with that load rating and a sidewall height of 104mm or less. If you want a tire between 225 and 245 wide, you could chose a 225/45, MAYBE a 235/45, or a 245/40. Tie in the wheel size and you can narrow down the choices by using the load rating.
However, if you have a tire with a large sidewall (>105mm), AND your tire load rating is many points higher than what you need (like a 96 instead of 90 or so) you'll have a punishing ride and possibly steering and other effects. I could almost guarantee that a 245/45 would be a nasty choice for any car that operates at a point significantly lower than the load rating.
Just would like to save you the cost and trouble of trying to do a straight replacement into something that might f*$k up your car pretty bad.
I know this because I know.... unhhhh... someone that tried to upgrade their tires on a car with an available run flat... $500+ later, that "someone" replaced their car back to non-runflats. And learned that there is more than just a straight substitution.