The GI1234567890 number identifies the box, and your account, this box can be switched to another address in the same node, or hub. Outside of that area, usually a bigger town or series of smaller towns, the box will shut off.
You can own your own box- You must tell the cable company you posses one and they are required I BELIEVE to activate service.
As for illegal black digital box, the only correct way to get digital service is so underhanded it would cost the technician you stole it from about $180 and possibly his job for letting it get stolen from his truck.
These cable company supplied boxes come preprogrammed, if you were to place an analog filter on the ingoing f-81 connection(place you screw the cable going into the box) and turn the box on for the first time, the box can't send out the "hey I'm on signal" and you get 55+ channels of nothing on- except really awesome cable.
I don't condone this activity and have never tried it.