can high frequencies damage a subwoofer?

Alpine guy is right, a speaker is a speaker.  It's not frequency that can damage one, it's power.

There are many reasons why you want to block higher frequencies from reaching your sub, but damaging the speaker is not one of them.

Here's proof that high frequencies can't harm a subwoofer:

http://www.realmofexcursion.com/videos/Adire/brahma12.13.wmv

The only speaker playing in that video is the sub.

I have to say I disagree as high frequency through a sub still puts the same power to it, but the cone travels less resulting in the coils to get hotter quicker which can cause warping. The sub is destroyed in a short amount of time, however this is ONLY if nothing but high frequency is pushed. The less high frequency you push to a sub the better.

This is why they have frequency responses.

This is absolutely incorrect.  Whoever told you this did not know what they were talking about.

Subwoofers have a very large coil of wire sitting around a large piece of metal which results in very high inductance.  Because of this, they have a built-in low pass filter.  This inductance combines with the DC resistance of the sub resulting in an increasing impedance with frequency.  This means that less power will be drawn from the amplifier at higher frequencies.