If the woofer cone vibrates after the signal is over, then that will appear as distortion--output signal varying from input signal. It will also appear in the various diagrams produced by REW as resonant ringing. A sealed design is one way to manage that, but for it to work, the compliance around the woofer cone has to be quite soft. The classic AR/Advent/etc. acoustic suspension speakers of the past used soft foam compliance around the woofer cone, where ported speakers can uses a stiffer (and more durable) compliance. At least, that's my experience.
I always seem to prefer rear-facing ports in ported designs, but I'm not sure I can defend that based on data and certainly my experience sample is rather limited.
But acoustic suspension speakers can also have unwanted resonances and ringing, which is where the term "one-note bass" came from. The term I've always used is "boomy".
And, of course, in the subwoofer range the resonances of many rooms will probably cause a lot more ringing than a one-note woofer.
The solution is not to simply roll off the bass, as a lot of stand-mount speakers do. The solution is to provide broad-banded and smooth response down to the bass region. A lot of speakers went to ported designs to provide more output with smaller drivers, but there are, of course, ways to do it right. I certainly don't hear any boominess in my Revel F12's, which have two forward-facing 8" woofers and a rear-facing port.
Rick "listening in my office to tiny Pioneer BS22LR speakers--no real bass below about 60 Hz but no port chuffing or ringing, either" Denney