Power Steering sudden failure: The steering freezes and unfreezes when the car is restarted.
Your Corolla has electric power steering like my '09. The rack and pinion assembly may be going bad but a bad alternator or battery can produce similar problems. Have the battery and alternator tested first. If nothing else you’ll eliminate a possible source and best case you’ll spend a lot less on a repair.
I am a little confuser by you saying it unfreezes when the car is restarted.
Has the car stalled, or are you shutting off the engine and then restarting it?
+1 to @davepsinbox_157004 My son’s 09 Corolla had a failing alternator, the first symptom was the power steering failing. The battery light did not come on until a few moments after. Is the battery original? If so might be time to replace it.