It's almost never a failure of the coil windings. The usual culprits are the semiconductors that control the firing of the primary. Heat is the enemy of semiconductors and the ignition module on a chainsaw is in a hostile heat environment, some are mounted right on the cylinder (really stupid) and others get packed in with gooey sawdust that insulates them from the cooling air off the flywheel. The worst time for the module is right after the engine is shut off after being run hot, the residual heat soaks into the module and no air to cool it, this is why there is a lot of advice to let the saw idle for a few minutes after serious cutting, to let it cool down a little. There are many grades of semiconductor quality in terms of heat resistance, military spec semiconductors are available to withstand extreme heat but they are very expensive so we will never see them on a chainsaw. The secondary of the coil transformer can become damaged if the engine is pulled over fast with the plug lead off and the ignition on, normally during a spark event, the voltage spike to fire the plug will rise until the plug fires and then will go no higher, but if there is no path to ground for the voltage spike it will rise to the maximum the coil can produce and that might be high enough to break down the very thin insulation on the wire in the secondary and could eventually lead to a trace path to ground and a dead coil. Taking these things apart is a waste of time, if a hacksaw is used nothing can be found that is recognizable and the few solvents that would dissolve the epoxy are so toxic you wouldn't want to use them if you could find them.
