Every training car has a second brake pedal on the instructor side, clearly marked, that can stop the car independently of anything the student is doing. It has never been needed for more than a gentle correction, and that is the point: it is there so it never has to be dramatic.
Cars are inspected on a fixed schedule and carry commercial driving-school insurance, which is different from and in addition to an ordinary personal policy. The roof sign identifies the car as a training vehicle to everyone around it.
It is also, quietly, a financial argument: many insurers offer a discount once a teen driver has completed certified instruction like this, because the data backs up what the second brake already tells you.
