Although complete brake failure is extremely unlikely it is a possibility. Obviously, if total brake failure occurs there has to be some alternative method of bringing the car to a stop.
If there is time, this is not so difficult. At high speeds, say above 80kph, the driver should change back at least one gear in a manual car and then ease on the hand brake. When the hand brake is effectively slowing the car the next lower gear should be selected, and so on until the car can safely be pulled to the side of the road. In an automatic, all that is required is that is that the selector should be slipped to Low and then the hand brake used as above. In most cases the gearbox will not immediately engage low range but as the handbrake slows the car, the lower gear will become effective.
But if there is no time for all this, then you have a real emergency and some sort of entanglement with the surrounding countryside would appear to be inevitable. If it is inevitable, it should be deliberate rather than accidental. As soon as the driver becomes aware that he has lost brakes, let's say on a long downhill run, he should steer the car broadside against a kerb or embankment and hope that the friction of contact will slow the car. In a corner, it is better to try to get around the corner than it is to let the car go straight ahead. If you are going too fast for the corner, chances are the car will spin and the act of spinning will itself take off a considerable amount of speed if not all of it. It all sounds very hair raising and dangerous and it is. But under such circumstances you have two choices- do something or do nothing. To my way of thinking it is better to try anything than do nothing at all.
Ultimately, you can spin the car deliberately. Such a practice is for an absolute last ditch effort only but, since it may save your life, it is worth knowing. The technique only applies where you drive a car with a handbrake that operates on the back wheels. The procedure simply requires that you pull on a small amount of steering lock to get the car turning slightly and then pull on the handbrake hard enough to lock the back wheels. The car will immediately spin and in spinning will reduce its speed surprisingly fast. Such a procedure obviously needs a piece of clear road. But in a brakeless car with a dangerous situation coming up at the very least it might reduce the impact of the impending collision.