Kaz, welcome. Even when the main speakers are connected through the sub, using the speaker level input and output terminals on the sub, this is simply a straight-through connection of the power and audio signals from your regular amplifier. The internal sub amplifier has nothing to do with the main speakers and only powers the sub driver itself.
There's no "stripping off" of any frequencies from the front speakers; they continue to get the full range of frequencies and the result is the same as it would be if you ran a separate wire from your amplifier terminals directly to the front speakers rather than running it through the sub terminals.
Even the audio signals that are directed to the sub amp itself by the branch of the wire from the input terminals are full-range, not with the bass "stripped-off". Since the impedance at the input of the internal sub amplifier is on the order of tens of thousands of ohms, essentially no power can get through, but the audio signal frequencies do. The low pass filter inside the sub(sometimes less accurately referred to as a "crossover")then rolls off those frequencies above the selected frequency on the control and only the lower frequencies are amplified by the sub amp and sent to the sub driver cone.
