There is a pin or slide and notch system that keeps the ignition switch locked in its different positions. This can fail if the spring that keeps the pin/slide cam pushed out so it will stay in each locking notch. Then it will not work properly and not stay in the notches much like a, "Ratchet".
There is a spring that turns the entire lock cylinder away from the start position. This is the last position on the lock that you have to turn a little harder to actuate. The reason it turns the cylinder away from the start position is to avoid the starter engaging during engine operation. So, when the cam lock for the cylinder fails, it will push it towards the, "Accessories" position when the key is removed.
I included the wiring diagram with the starter switch so you can see this direction and see that if the switch catches any of the continuity of the accessories circuit, touches any of the metal together, it will drain the battery.
So, the starter switch needs to be replaced. It will come with a new set of keys and will require taking the steering wheel off and some other components in the steering column to replace it. This also includes the airbag. You must remove the battery to work with the airbag, but they can still be dangerous. They have been known to go off when out of the circuit and possibly thrown around during the time it is out while you are working on the car. The other issue is making sure you re-install it correctly.
Right now your car is also at a security risk due to the broken cam slide. Make sure that the car cannot be started without the keys because this can happen as they keys are what allows the cam slide to un-luck at all from the, "OFF" position.
You might also stall during operation as the failed cam slide may allow the keys to move away from the, "RUN" position. This can also allow the steering wheel to lock in place while moving.
I know this is more than you expected, but I want you to be aware of all the safety issues involved with the current condition of the starter/ignition switch and the possibilities that might put you at harm. Also, working with airbags generally requires a repair tech that is especially certified in airbag circuits and repair. It can be dangerous to work with and if it fails in an accident it can lead to injury.
So, it is important you know these facts.
If you have any questions, please let me know. I will keep an eye on the post and get back with you ASAP.