What happens when you put 20 Hz. into a speaker that rolls off at 40 Hz. is simply this: the cone moves a lot, there is some second, 4th, etc. harmonic reproduced, your amp works hard and may have reduced headroom if this coincides with a peak.
MOST speaker systems do NOT have significant output below 40 Hz. Period. In order to produce bass below 40 Hz. you need a few things that most speakers can not and do not have. That is in specific enough surface area & excursion to move the required air, which also requires a LARGE cabinet size.
It is true that you *can* make a small speaker that will have output that low, but it will NOT be able to have normal levels of sensitivity or output, or else it will have output below 40 Hz. that is WAY down from the midrange level. So, in practice, most speaker systems are not able to do much below 40 Hz. In practice, sorry to report, most have difficulty making it all the way to 40 Hz. 20 Hz is usually out of the question.
There are some exceptions in this regard, but they are rather few and far between. Many that advertise output in this region do not produce much usable bass unless they are set up in a particular manner or room postion/volume.
With the advent of the latest crop of high power handling/long linear excursion woofers we can expect to see much better bass response and lower F3 points in commercial speakers in the near future... but the price for this is the need for POWER on the amp end (and in the case of sealed cabinets, EQ AND POWER).
To a great extent, this reality is the basis for the existance of a market for what we call "subwoofers."
_-_-bear