As you go up the frequency range from 0 to 20kHz, in an ideal world speakers and amplifiers etc would respond uniformly so that there is a constant output no matter what the frequency. Amplifiers have to cope with a wide range of frequencies and they are designed to have as flat a response as possible. Speakers are limited by their physical size. A tweeter being small will have a maximum response in the high range at several thousands of cycles per second (kHz) whereas a woofer being large will respond more to frequencies at the low end e.g. 100 cycles per second?
As you move away from this peak either up or down the frequency range the response tails off until at a particular frequency the level is 3db below the peak. These are the 3db down points (-3db) and it is the range between these points that is defined as the bandwidth. The speaker will respond to lower and higher frequencies, the response does not just stop at these points so you will get a response of some sort even at 20Hz but it will be less than it is within the specified range of 26 to 200Hz.
Crossovers are used to enable high frequencies to be applied to the tweeter and low frequencies to the woofer, etc. There is no point in applying power to a speech coil without the benefit of some sound being emitted. It wastes power and could damage the speech coil. Crossover filters do not cut dead at a set frequency. The response overlaps somewhat. There is, as far as I know, no such thing as a 'Brick Wall Filter' where the roll off in response is in effect infinite.
As to the limit, well if you find the cone attached to the wall on the other side of the room I think it would be safe to assume that you have overdone things slightly!
Hope this helps