1996 Jeep Grand Cherokee stalls when brakes are applied

definately a vacuum problem, try changing your pvc valve its under $5.00 and easy

simple test
ut the hand brake on and start the car
idling ok --good --apply the foot brake-- idling bad --replace the brake booster
check for other vacuum leaks including transmission actuator hose , dash vent controls hoses

Is the MIL ligh on? have you checked for codes? if no codes stored then you have a vacume or fuel issues. Replace the IAC idler air control valve and or look for vacume leak.

Try looking at your air filter. You could have a vacuum leak, like you already said. Also, check your coolant sensor and intake air temp sensor, if equipped.

replace the mass air flow meter.

I would say that you have WARPED DISC BRAKE ROTORS which is the beginning and possibly all of your problem. It he suspension such as STRUTS are weak, that will elevate the problem. Hope this helps.

Is it a consistent pulsing or does it get faster as the speed goes up?

check the vacumm hose to the brake booster. it might have a leak causing a slight increase in idle and a kill prob when brakes ar applied. good luck

change the idle control valve located at intake manifold.

This is caused by by a bad ignition switch. According to the dealer the ignition switch contains an antenna that many of the sensors use to communicate with the vehicle, as well as the key fob. When the switch starts going bad the vehicle computer losses communication with these sensors and starts producing codes which include the 4wd and the electronic brakes. My fiance has had the same issues with her Grand Cherokee as well as the key fob not working, the remote start not working, the service engine light comes on, the door chime will sound when the key is NOT in the ignition and the lights are NOT on, as well as numerous codes usually relating to loss of communication with one system or another. All of which are fixed once the ignition switch is replaced. Unfortunately, this usually only fixes the problem for a short time (weeks or maybe a few months) before the piece of junk ignition switch fails again and it all starts over.