Two things happening:
As frequency falls below the tuning frequency of the reflex port, the port/cone resonance decouples, and the driver loses its internal acoustic load, allowing the cone excursion to increase quickly with falling frequency.
BUT, at such a low frequency, a small diameter cone has very little acoustic impedance and cannot grip the external air to create a sonic impulse because of the very slow velocity of the small cone at low frequency. It is moving but it can't grip the air that low, so you can see it move, but it is not making any sound. If the cone were much larger it could grip the air and make sound at that low frequency. Likewise, if the small cone were playing much louder (larger excursion,) the velocity would increase enough to catch some air and be audible, though it would sound like mud anyway.
As you suggest, you could increase the length of the port to lower the port tuning frequency, so the driver does not decouple from the load of the resonating port, but lengthening the port will have negative effects on sound quality at higher frequencies.
If it is a commercial speaker the port tuning is probably set correctly for the intended purpose of the speaker. A small speaker is not intended to be played loudly far below the port tuning frequency. You can break the driver if you allow it to bottom out due to too much power and no acoustic load below the tuning freq.
Never heard it called cone shake, so maybe you're trying to describe something else. Hope this helps
