A crank sensor telling the computer that the engine isn't turning can trigger the ASD.

Again, if the crank sensor maintains connection to the computer but fails to pick up the signal from the reluctor wheel then the car will assume the engine has quit running.
A fault code will only be stored if the crank sensor fails to report to the computer.

That's what trips up a lot of people. A bad sensor will not always trip a fault code. Sensors have two jobs.
1) Monitor the engine for it's designed purpose.
2) Report it's findings to the computer.
No matter what it says, if it talks the computer will think it's okay.

If an O2 sensor fails to detect unburned oxygen it will tell the computer to change the mix. The computer doesn't know it's gone bad and will assume the sensor is reading correctly. The computer will only point a finger at the O2 sensor if it quits talking.