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If there is a leak in the brake booster, or the vacuum hose or a cracked, ruptured or leaking diaphragm it can cause a stall. It may only be leaking when the pedal is depressed.
Is it running well? If it is not running good it will not make as much vacuum and hitting the brakes will use up all the available vacuum and stall the engine.
Shut the engine off and immediately pull the one-way valve off the booster. If the booster is holding vacuum, you will hear a loud whooshing noise.
If no noise or very little is heard, check the one-way valve to see if it is functioning properly. Hold the valve to your mouth and put suction on one side and then on the other. If air can be sucked through the valve in one direction and not the other the valve is good. If air can be sucked through both sides it is bad and needs to be replaced.
If the valve is good then the booster is bad and needs to be replaced. The reason for the failure could be it is defective or it could have a leaky master cylinder. Look at the mounting surfaces where the master cylinder mounts to the booster. If there is any brake fluid on the booster the master is leaking into the booster and causing deterioration of the diaphragm. Replace the master cylinder as well, for it will ruin the new booster.