40hz ratings/speaker response

Hi, as a neophyte to the technical end of this wonderful addiction, I am curious. If a speaker's frequency response capability is rated to say 40hz or above, what happens to that sound that was recorder that falls below that range? Say for instance the lower octaves on an accoustic piano, or a cello, electric bass etc? And again, what happens to a speaker, with the same rating, if the volume is "pushed" to hear and feel music that has a lower range?
Curious