The purpose of the "dead cut" magneto check after start is two fold in the sense that when selecting an individual magneto there should a) be some drop but b) the engine does not stop. a) confirms that you do not have a live mag b) confirms that you do not have a completely dead mag!
This is what I've always understood the purpose of the dead-cut check to be. However, if you have badly fouled plugs then this can cause the engine to stop as well. I discovered this one when preparing for a night flying sortie. When I did the post-start dead-cut check the engine stopped when I selcted one set of mags. I switched everything off, went back to the clubhouse, and reported the aircraft U/S with a dead mag. One of the instructors went out to check (why do they never trust us?) the aircraft. He confirmed that the engine did stop on one of the mags, but after running at 2000rpm with the mixture leaned out for a few minutes, the problem had gone, showing that it must have been due to fouled plugs.
Brooklands