By 8100 I am guessing that you are referring to an 8.1L engine? To answer the question though your braking system is a power assisted system. Depending on application engine vacuum acts on a diaphragm in the brake boost canister helping to apply power to the actuation rod that is pushing on your master cylinder piston. The other application is a hydro boost set up where Power Steering fluid is routed to an accumulator and is used in much the same way. The brake pedal is pressed and a rod presses on the master cylinder piston, this opens a valve allowing pressure stored in the accumulator to act on the piston. In either application, when the engine dies there is no longer a supply of vacuum or power steering fluid to create pressure for the power assist. It feels like you have no brakes but you still do. Just press harder on the pedal.
Is your brake pedal hard ? If so replace the power brake booster. It sounds like you have a major vaccume leak in the booster when you apply the brakes. Power brakes work off of engine vaccume. If the dieafram is leaking vaccume when you apply the brakes it leans the engine out. ( creates a major vaccume leak ) and engine dies. Hope this helps.
When the engine dies, the power steering and vacuum assisted brakes are no longer receiving the "help" from the engine. Find out why the engine is stalling and the rest of the problems will go away.
Probably needs a new Idle speed sensor
The idler pulley has nothing to do with the brakes. If the idler pulley is bad it could throw or break a belt, and then your engine will stop.
Have vehicle scanned to determine problem and recover codes Could be a bad coolant temperature sensor
If you have a check engine light "on" then you need to have it scanned for codes. It could be numerous reasons such as a vacuum leak, loss of fuel pressure, flooding,and the beat goes on.
Timing belt.
engine
It's probably your IAC.
If the engine light is coming on at the same time as it the engine dies and I am guessing it starts again. It may be your electric fuel pump. You left too little information about the sympton as it could be a number of things. The check engine light will come on if the engine dies. it could be your o2 sensor
You are losing spark or fuel.
Check the throttle position sensor