With the cylinder removed there is no easy way to turn the switch it would normally operate to the "off" position.
It may not be connected right.
You need to replace the ignition switch. Too much play in it.
That's called dieseling, and the main thing that causes it is improper ignition timing.
The ignition cylinder is the part you turn your key in to start the car, this is in its housing.
It depends upon cylinder in car. 3 ignition coils - 3 cylinder engine. 4 ignition coils- 4 cylinder engine.
Sounds like the ignition has become worn and will not automatically shut the car down. You may want to take the car to an auto mechanic to have them check the ignition cylinder and replace it for you if it bugs you. While sometimes convenient, this could be dangerous.
Most likely is a bad ignition switch or lock cylinder.
when my car did this it was a blown fuse
You should check the wires that are in the steering column to the ignition lock cylinder. They tend to break easily.
Need to replace the ignition switch.
Insert the ignition key into the ignition and turn it to on, the alarm should shut off.
It's the cylinder or the key is worn down. Once I ran into a problem where the cover on the wafers rose up and was hanging in a slot in the cylinder housing, but the key would turn but not far enough to start the car. But if it wont turn, I would suspect the key or something sticking inside the lock.