So I had a customer who was rich and lazy and didn't want to get out of his bed to press anything or plug something in so everything kind of had to be within reach of the bed or controllable from a remote.
So my task was to make some wireless headphones cut out the sound from the surround sound receiver to the ceiling speakers when they were active but being that the source of audio was from the headphone jack on the surround reciever located in a closet that required walking, it was too incovenient of them to plug the 1/4" plug in each time to the headphone jack and leaving it in would result in the sound not working on the ceiling speakers. So I hacked the surround sound receiver and modified the headphone jack's switch that detects when plug is in and routed that to a relay that I could remotely control that I mounted in the surround receiver. I made a custom cable that I ran under the house going from the receiver to a wall jack by the clients bed. Two wires for relay coil, Three shielded wires for Left, Right and Signal ground. I also hacked the base of the wireless headphones as there was a green LED that would light up when the headphones were removed from base and active. The green LED was controlled by an output pin of a processor in the Base unit. I tapped into that line with a resistor ran it into an optoisolator whose output I then ran into a transistor with a 12V output to trigger the relay inside the surround receiver and trick it into thinking the headphone plug has just been plugged in even though it was plugged in the whole time.
So the point is, with a little modification to the cable box, assuming there is an LED that lights up only when the box is powered on or some other kind of logic output you can find when it's powered up, you can utilize that trigger something else. Usually the boxes even when powered off, will have some kind of standby power like 5V DC you can use to power a monitoring circuit. So if monitoring the Power LED and circuit detects it off, it can trigger a delay which when timing out triggers a relay with contacts feeding to the power button on the box which would be as if someone went up and pressed the power button on the box.
This maybe a little complicated, but can be done. I've done this trick many times..