MOst likely your EGR valve is sticking open. This would cause the sputter stall condition. Have it removed and opened manually with a screwdriver. If it sticks open that's your problem
If you have the 99 -02 Cougar replace the TPS (throttle positioning sensor) on the throttle body.
The year, make, model and engine info would help, but I would start with replacing the fuel filter.
Symptom of bad fuel filter= stalling when slowing down to stop at lights or stop signs.
I just put a new battery and alternator in my car, but when i put it in gear or start slowing down to stop..the car die out. Also the brake light is continely on.
At this time (August 2012) unfortunately, no. Research is ongoing to find ways of slowing or stopping damage to the brain caused by HD.
The steering wheel shimmering could be warped front rotors, when slowing down. The stalling when slowing down could be a bad fuel filter.
If it is a stick shift or manual, you may be stalling it. a way to stop this could be to place the clutch all the way to the floor.
I would check for any fault codes first with an obd tool, is the check engine light on?
slowing down.
Transmission may not be downshifting properly or one of the belt driven acessories could be putting to much load on engine. See if it happens with A/C, defroster and vents off, if not it could be your A/C compressor stalling the engine
its when something is slowing down
Gradually slowing down is 'decelerating'.