A hall effect sensor is generally used to indicate an event occuring with some frequency such as camshaft, crankshaft, or distributor position. It produces a square wave output corresponding to a magnitic field passing in close proxsimity to the armature of the sensor. It could also be used to detect wheel speed but more than likely, wheel sensors (like those for ABS) will be a variable reluctance sensor. This sensor would be pointing to a toothed wheel and generate a sine wave whose frequency corresponds to the rotation speed of the wheel. I believe that my 190E has one pointed at the teeth of the flywheel. If a wheel has a tooth missing, the waveform could also indicate a particular event such as top dead center.
If a hall effect was not working, the engine wouldn't stall at just idle. I would look at the air flow meter. I don't know if your car uses a vane or a hot wire to sense air flow, but if isn't working, the engine controller will give the engine the wrong amount of fuel and possibly stall the engine.
I had one car with a vane meter that would get oil in it and stick(from the turbo I guess) and not open correctly at idle. I would spray the vane with carb cleaner and it would be ok again.
'05 E320 CDI - 86,000 miles
'86 300SDL - 360,000 miles
'85 300SD - 150,000 miles (sold)
'89 190D - 120,000 miles (sold)
'85 300SD - 317,000 miles (sold)
'98 ML320 - 270,000 miles (sold)
'75 300D - 170,000 miles (sold)
'83 Harley Davidson FLTC (Broken again) :-(
'61 Plymouth Valiant - 60k mikes
2004 Papillon (Oliver)
2005 Tzitzu (Griffon)
2009 Welsh Corgi (Buba)