If you remotely start it and don't actually get in and press the start button it will shut itself down, I think in 10 minutes. As far as I know we don't have a direct way for remote stop, but OnStar in cooperation with law enforcement near by can to my knowledge if you have an active OnStar subscription).
I love to see a bunch of folks looking at my C7 and start it from afar. The looks on their faces is astonishment I parked the car where I could see it while we were eating. I hit the remote start and people close though they had done something to create the start. I laughed and they laughed. --priceless. cutnout aka Charlie( a little bit of the devil at times)