Car runs fine till it is turned off

For some reason aleros have this problem every once in awhile. It might be the security on the alero. What you would have to do is turn the key all the way to accel i believe right before you start it and let it sit for about 13 minutes. affter this the security will recognise itself and start your car

Check the electronics,cam sensor or crank sensor these are the culprits.

Yes there is one and I think it is under the hood on the firewall.

I had the same problem it was 2 bad injector they where shorting out it would run for awhile shut off and not start for 2 hours

This sounds like a hot fuel pump issue. The pump is getting hot on the circuit and is cutting out.

If it is a 3.8 engine change the crank sensor,they go bad on the 3.8 engines.

The engine in this car is controlled by a computer, whenever you have a stall like this the computer will record a fault code for the event, you must have the system scanned to get that code, then based on the code you start the diagnostic to repair the problem, which in your case is likely a CKP sensor. But that is just a guess, don't replace anything until the testing confirms it is the problem.

Is then engine light ON? if so check for codes and if not then it has to do with fuel/air delivery.

Sounds like the fuel pump has an issue with a safety on the pump itself.

I would be more suspicious of the fuel system. Have you changed the filters lately? Do you have a 6.2 or a 6.5?