Would a Crank shaft position sensor make car shut off?

Yes, a faulty crankshaft position sensor (CKP sensor) can definitely cause a car to shut off, or prevent it from starting altogether. The CKP sensor tells the engine's computer (ECU) where the crankshaft is in its rotation. The ECU uses this information to time the fuel injection and ignition. Without this crucial information, the engine can't run properly, and will likely stall or fail to start.