I am currently searching for a Chevy LFX for a project track car and there are plenty available on the market from the yards. When looking at collision photos from the donor vehicle, I generally favor rear impact as that should minimize the risk of damage from the collision. Side impact is next best and then front impact with no air bag deployment. Front impact with airbag deployment has risk and I also have seen some roll-over vehicles.
My question: In the event of a rollover in a modern car, does the engine die immediately or could it run for a few or many seconds upside down with oil starvation?
Typically the failsafe is when an airbag goes off it kills the whole car.
^Yep it cuts power to the fuel pump, so the engine could only run for maybe 3sec at idle after that.
Thanks - that helps keep more options open 
Rear impacts can potentially shove the driveshaft into the transmission.
The fuel pump typically stops pumping fuel when its pickup is at the "top" of the tank, allowing the engine to stall. This is considered a problem for aircraft but is acceptable for land vehicles 
Airbags may not even go off. I have witnessed a rollover collision, stopped to help, and noted that the side curtain airbags did not go off.
As noted, rear collisions can damage the transmission. Side collisions can also break things like motor mount bosses.
Really, the best option is to grab an engine off the shelf with a warranty.
