How to hook up a subwoofer with an integrated amp?

A straightforward way to do it would be with these adapters. It would minimize the length, and cost, of either long interconnects or speaker cabling.

It depends on the inputs accepted by your sub. I assume your sub will have separate inputs for the left and right channels, and it will somehow combine the signals internally into a mono bass (sound) output.

The Avatar appears not to have a line level output. It does have a tape out, but its gain is not regulated by the Avatar's volume control. The good news is that you have a volume control on the Cary. So, one way to go would be to connect the sub's line level input to the Avatar's tape output and use the Cary's volume control. With this, the Avatar's volume control should be turned up to a unity gain level to match levels between the sub and the main speakers. The primary drawbacks of this setup would be the inconvenience of using the Cary's volume control instead of the Avatar's and also the need for potentially long interconnect cables from the Avatar to the sub, possibly resulting in signal loss or degradation.

If your sub accepts the output of a power amp, i.e., speaker signal, then you could run a pair of speaker cables from the Avatar's output to the sub. This would be in parallel (electrically parallel) to the existing cables running to your Sonus Fabers. Depending on where your sub is located, you could run speaker cables from the Sonus Fabers' terminals to the sub instead. If you do it either of these ways, I would recommend hooking the speaker wires to the Avatar's four ohm tap to begin with. (The Grand Piano's are rated at eight ohms, but the effective load will drop when you add the sub to the circuit.) The primary drawback to this setup is that the signal to the sub may not be as perfect since it has gone through the Avatar's power amp stage. Potentially, the power amp may color the bass frequencies, and/or the bass frequency signal sent to the sub could be colored by the interaction between the amp and any impedance variations in the Sonus Fabers at the low end. Personally, I would choose the tape output method. Good luck.

Thanks James for your input, especially with the tape out. Unfortunately, my Cary (303/100) doesn't have a volume control (unlike the 306), therefore the tape out option may not work.

So, between using the Y adapt and running parallel speaker cables, which one is lesser of the evil? Or the parallel run, besides the drawback that James mentioned, what about cross over concern sonically? i.e. say the subwoofer's cross over will fiter out any signal above 80Hz, but what about the existing speakers, since there is no cross over that "tells" them not to drive below 80Hz. Would that be a concern, especially within the frequency range of, say 40 to 80Hz, when BOTH the SW and the speakers are driving together. Any inputs? Anyone?

I would suggest running Y instead of speaker cables.
Since most preamps out there with 2 sets of output which the design just basically "Y" inside the chassis anyways, I don't think Y-ing the line level signal will accfect the sound as mush as Y-ing the speaker cable signal.