If the HPF is variable it's generally adjusted to taste. That means the frequency can change depending on the room and you tone goals.
However, an HPF does have an important role in protecting your woofers from overexcursion, especially in ported designs.
The excursion plot of a woofer in a ported design has sort of an S shape. The precise shape of this curve is determine by the Thiele Small characteristics of the driver and how the box is tuned. In other words, put the same driver in different boxes and you get a different a different excursion plot and also a different frequency response.
These cone excursion and frequency response plots are for an Eminence 2512 II in a larger ported cabinet:
Ref:
290-593--eminence-deltalite-2512-cabinet-design.pdf (parts-express.com)
In general: Starting around 500hz, as the frequency goes lower, cone excursion increases. The excursion continues increasing until a bit under 100hz, and then it starts to decrease. The reason this reversal occurs is because the port is starting to become active.
The port tuning frequency (Fb) for this design is 44hz. You can clearly see this in the excursion plot; it's where the excursion dips. At 44hz, the port is providing maximum suppression of cone excursion and also producing most of the sound.
Below Fb cone excursion increase dramatically and acoustic output of the system drops (typically) by 24dB per octave. Because of this it does not make much sense to feed the system power very far below Fb. Doing so does not produce any usable output, and it puts the woofers at risk from over excursion.
For context, the 2512 is rated for 250W RMS / 500W Program and has an Xmax of 4.9mm. But in this box the 2512 is mechanically limited to 125W and requires a steep HPF set no lower than 35hz.
Ref:
290-593--eminence-deltalite-2512-spec-sheet.pdf (parts-express.com)
If you look at the cone displacement chart, you will notice the driver exceeds Xmax at about 35hz. This is where the trace turns from black to gray.
If you adjust the HPF to 35 hz, it means it is reducing power by 3dB at 35hz. So if you are feeding the speaker 125W at 35hz and apply a 35hz HPF, the power drops by 3dB to 62.5W.
Keep in mind that an HPF is not a limiter. So if you crank up the gain by 6dB, the power level will rise to 250W.