What kills speakers? The answer: Overpowering.
Let me explain. A radio, of any size is simply taking information, be it from the radio waves, a cassette tape or the D/A converter of a CD player, Minidisc or DAT, and then proceeds to amplify this signals voltage and current levels to a point where it will cause a speaker to move. In a typical in-dash CD player, there is a small Integrated Circuit which does all the final amplification (after volume, bass, treble, etc.). The best of these chips make a real world 13-18 Watts of true properly rated power. Any claims beyond that contain high levels of distortion, noise, and are in a limited frequency range.
We call upon our CD player to drive 4 or so speakers in a car. Each should get this max of 13 or so watts before distortion sets in. Lets look carefully at this distortion.
Clipping is the result of asking an amplifier to try and amplify a signal to a point higher than it is capable of. We know speakers move back and forth. The amount by which they move is determined by how much voltage we apply to the speakers voice coil. If we can't increase the voltage, then the speaker will move no further. The problem is that which we are listening to music and suddenly a deep bass line kicks in, the speakers are asked to move much further to reproduce these low frequencies. All amplifiers have a maximum output voltage (one positive, one negative). An amplifier can not put out more than this voltage. Any signal that tries to go beyond this voltage level simply stops there. The output voltage stays at the maximum until it drops back into the standard operating range. The motion of a speaker cone attempts to follow the output voltage of an amplifier. Once the speaker has extended to the point that equates to the maximum output voltage of the amp, it will go no further. The speaker cone sits still until the output voltage comes back into the operating range of the amp.
What can you do to prevent clipping. Three options really, reduce the amount of bass in the signal, turn the volume down, or get more power. Bass frequencies require the largest speaker cone motion to reproduce, and as such, require more voltage from your amp. Less bass means less voltage (as a rule of thumb). For every increase in output of 3dB, you need to double the voltage coming out of the amplifier. If you have a more powerful amp, you can push the speaker cone further, just watch out for the physical limitations of the speaker.