Is it legal to turn off someone else's car insurance without their knowledge?

There's probably more that you are not telling us in this question. If it's your car insurance, then no, the insurance company will send you a cancellation notice before cancelling your auto insurance. If you illegally have your car on someone else's policy, didn't pay them, and they removed your car from their policy then yes. The only thing is they never should have put your car on their policy but that is as much your fault as theirs. An individual has no requirement to notify you when they decide to make a change on their insurance policy.