A braking system for a vehicle, which includes a control system configured to: actuate a pressure generation device in accordance with a braking request signal to generate the brake pressure; ascertain an operational state of the pressure generation device; ascertain a position of a displacement piston of a brake master cylinder based on the braking request signal; and couple a pressure modulation device to a brake master cylinder volume and actuate the device so that the pressure modulation device conveys brake fluid out of the brake master cylinder volume into the wheel brake circuit, if the operational status of the pressure generation device is ascertained to be nonoperational and the displacement piston is in the idle position.