Inside of those headphones is a cone, that cone is responsible for moving air at the frequency that the music is playing. For example, a certain part of the song might be oscillating the cone at 100Hz or 100 times/second. As we all know songs don't just have one sound the whole song. The frequency could be changing or you could have multiple frequencies. That's why you can hear both, for example, a clarinet and a trombone. Base tends to be very low frequency and at higher voltage. Those cheap, as you said, headphones may only be able to play, for example, over 100Hz @ a certain voltage. So when the base drops, per-say, the specification of the headphones are being maxed out. Depending on how maxed out they are, they could either give up or blow.