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Originally Posted by
Archaea 
What happens when an amp clips on subs?
To coin a phrase, "That depends".
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Is it like a short circuit where the amp drops full power into the load?
Not usually.
For openers, a subwoofer usually presents at least 3 different kinds of load depending on the frequency. Below resonance, it is varying from a resistor at DC to a inductor just below resonance. At resonance, it is like a high value resistor. Above resonance it is like a capacitor sloping down to the point where its voice coil reactance starts taking over and it again looks like an inductor.
These days we have the option of making the amplfier clip in its input DSP in which case the amplifier continues to drive the speaker with a low source impedance. Or, we can let the output stage clip, in which case the source impedance of the amplifier looks more like a diode. If the amplifier's output voltage is appreciably below VCC then the output devices are saturated and act like low impedances. If the amplifier's output voltage is near or above VCC the amplifier's source impedance will be high unless there are diodes that clamp the output to VCC.
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Two Scenarios
You have an amp that has N power. You also own a couple of subs that can handle different power loads. One can handle N power x2, and another sub that can handle < N power.
Say you drive the amp load to clipping.
The sub that can handle N power x2 will do what?
Will it make a bad sound? will the amp just power cycle or trip a breaker?
The sub that can handle < N power will do what?
Will it make a bad sound? Will it blow the driver? Will the amp just light up the clip lights? Will the amp trip a internal breaker or wall breaker?
The problem here is that you are presuming that the driver's power limits are relevant to the question you asked. You asked what happens when an amp clips, and then you start talking about the load. Amps are sources and speakers are loads and to a large degree their operation is separate.
Speaker drivers are unlike amplfiiers in that they don't change their operating characteristics rapidly when you increase the power you apply to them. The power handling capacity of a driver has both excursion limits and thermal limits, but compared to amplifier clipping, both limits are soft and spongy. The transition between them is dependent on signal frequency, and even that transition is soft and flexible.
For that and other reasons, speaker power ratings are more complex, vague, and pften can be generally violated without the kind of harsh short term effects we see in power amps.
Of course, good amplifiers are almost indestructable, while any speaker can be destroyed if you work at it, or are merely careless. If a speaker doesn't make ugly noises or burn up, its power ratings can be pretty much ignored. One is wise if one sizes speakers so that they either make somewhat ugly sounds or just keep on choogling, when the amplifier totally runs out of gas. A just barely undersized amp for the speaker at hand is a thing of beauty.