This sounds very much like a washer problem.
I think you have installed the protective washer between the clutch and oil pump wrong side up.This restricts the independent movement of the worm gear, which in causes the same to happen with the clutch drum.The result is the clutch drum is constantly locked to the crankshaft and if the brake is put on, the engine stops.
The Remedy?
Remove the clutch, re-install the washer with the Stihl logo facing towards the oil pump.
Make sure that the clutch assembly is free of too much wear and does not have any missing parts or damaged parts.Also ensure that the part of the drum which goes onto the crank shaft does not have too much wear.To check this, fit the sprocket needle cage and drop the drum onto the shaft wrong side up.Check if the drum tilts too much on the crankshaft, if yes, replace the drum(not available by itself, but as part of the rim sprocket kit)
Refit the clutch assembly and clutch drum.
Rotate the drum by hand to ensure it is running free of the crankshaft.
Start the saw without the bar and chain, with the brake in 'off' position.
The drum should come to a stop easily at idle speed when you use a finger against the outer edge of the drum.
If this is possible, your saw should not stall in idle with the brake on.
Joe