Chrysler delivered eight cars to race teams and both Lee and Richard Petty received a car. In the 1960 race, Lee was in number 42 and Richard in number 43. The 43 car was wrecked during the race. That's the car you are referring to. I heard that parts from it made their way into the 43JR Barracuda in 1965.
For the 1961 race, Lee ran as number 44. He won that race, which ironically was the last win of his career. A short time after he had that spectacular crash in a full size Plymouth and announced his retirement. That 44 car may be out there somewhere.
The Compact Class Races on lasted two years. I have documentation of some of the cars being used later at Watkins Glen and other venues. I have a copy of an ad from one of the magazines of the day offering one of the cars for sale. So I don't know if any of the 8 Valiants exist today. It would be cool if some did.