OK.......if you drive an amp to clipping, the resulting wave will have more effective power than the amps rated output. This is because the waveform will have flat, squared off tops and bottoms, and the speaker cannot physically follow that signal. When the signal squares off, the speaker cones inertia will cause it to continue in the direction it was going for a bit - it can't stop it's motion on a dime. It's like accelerating a car at full throttle for 100 feet and then trying to stop it in one inch.
So, if an amplifier is rated to put out 300 watts at .5% distortion, when you drive it to 5% distortion the speaker effectively sees a lot more than that.
You probably won't fry the voice coil this way, but you certainly can push the speaker past it's mechanical limits if the amp is rated to put out anything near the speakers limit. Whether you cook the voice coil with excessive wattage or damage it mechanically, it's still a blown speaker.
So, no, you can't kill a 400 watt speaker with a 10 watt amp, but you certainly could with a 300 watt amp, maybe a 200.