There are plenty of powered subwoofers available with speaker-level input connections. The input from your receiver/amp is full range. The subwoofer then filters out the higher frequencies with its low-pass filter, so that it is only reproducing the lower frequencies. All powered subs have a low pass filter. It is usually adjustable, to assist in integrating the subwoofer with the main speakers.
Of those with speaker-level input connections, many also have speaker-out connections. In most of these, the speaker-out connections are there only as a convenience, allowing you to connect your main speakers from the subwoofer instead of the receiver. The signal simply passes thru the inbound terminals and then on to the outbound terminals. In this case, you would not be able to run the subwoofer and the main speakers independently, as opposed to using the A and B speaker terminals of the receiver. (A for the mains and B for the subwoofer).
Of the subwoofers with both in and out speaker-level terminals, only a few (very few) of them provide high-pass filtering between the inputs and outputs. In this case, a high-pass filter removes the lower frequencies from the signal, thereby relieving your main speakers from handling the lowest frequencies. These will be handled by the subwoofer alone.