This may or may not be true. I saw it on Quora and decided to post it, as it could not hurt to try it. It would be just as applicable if you burned your brakes up decending.
You’re going downhill and suddenly you realize that you have no brakes. You panic at first and start hitting the brakes, again and again, you freak out, then you start asking yourself; “what should I do now?”.
First, you have to be calm and start thinking slowly of the next decisions you need to make. No brakes mean that you have both your engine and parking brake left to help you stop, the trick is to use them both correctly in order to safely stop.
Fasten your seatbelt and get ready!
Assuming you have a gasoline-powered automatic transmission car, first of all drop down 1 gear and check where the RPM of the engine is at, you need to higher your RPM to approximately 3000 or 4000. After you do this start turning on your headlights, fog lights, brake lights, hazards, dome lamps, radio, phone charger and any electrical accessory you can reach (these will put a load on your alternator which helps your engine to brake), next turn on your A/C full blast and make sure your compressor is running (the compressor will greatly help your engine braking), roll down all your windows (they will increase the air resistance on your car which helps you slow down faster at higher speeds). Now after you do all these steps you will feel that your car is no longer accelerating and in fact, it starts slowing down or at worst case, its speed will get steady.
Now start engaging your parking brake very slowly until you barely feel your car starting to slow down (do not engage your parking brake too much, the risk of locking up the wheels and losing control is so high).
Now after you start engaging the parking brake your car will decelerate at a faster rate and your RPM will start decreasing more and more. Keep you RPM at higher than 3000, if it gets lower then it is time to drop down 1 more gear. Keep down shifting progressively until you reach the 1st gear, by that time your speed will be at around 10–15 mph, you are safe now. Go to the edge of the road and come to a stop by engaging more of the parking brakes until you stop.
The same applies in a manual car but you have to be more cautious in downshifting as you might over-rev your engine and lose control. Automatics won’t downshift if the gear you selected will over-rev the engine.
P.S.
Do not turn off your engine until you come to a complete stop.