Potentially fatal damage; depending on how much over we are talking, the type of the signal (test tone or music), the method used to derive the rated power handling, the installation/enclosure, settings of the system (gain, EQ and such), etc etc.
Keep in mind that the mechanical power handling of the subwoofer is completely installation/box dependent. It is entirely possible to mechanically damage a subwoofer with it's "RMS rated" power. The rated RMS power handling is sometimes, but not always, a thermal power handling limit only. But, in either case....the installation/enclosure will always dictate the mechanical limits of the driver.
Also keep in mind that you can use a larger than necessary amplifier, and not drive the subwoofer with the amplifer's full power output capabilities. So, even if you have a "1000w RMS" amplifier, it does not mean you are actually using the full 1000w of power. Ever heard someone say something to the effect of; "Yeah, that 300w RMS sub handled my 1000w RMS amplifier just fine....I just had the keep the gains really low and turn down the subwoofer level on my deck" ? The sub wasn't handling anywhere near 1kw of power, because it was setup in such a way that the amplifier was not delivering anywhere near 1kw of power.
And that doesn't even begin to take into account the transient, dynamic nature of music and it's affect on the output of an amplifer/power handling of a speaker.
As you can see.....there are far too many variables to state with a complete sense of certainty how much power a given subwoofer will handle in a particular situation.
Though I agree with Supa.....buy a larger than necessary amplifier if upgrading subwoofers is in your future.....you can always limit the amplifier's output via different methods if necessary.