To bring you up to date: I have 4 undercabinet lights in my kitchen, high voltage, that are attached to a dimmer and run on a lamp cord that is strung in an unknown pathway through the wall. The dimmer and one of the small appliance circuits are on the same circuit.

The undercabinet lights stretch in an L formation with one on one side of the kitchen and the others on a different wall but they must somehow be connected.
Do you think it might be feasible to somehow abandon the lamp cord in the wall and not have to worry about removing it?

I hope you don't think my question is too silly.

If so, yes, you can disconnect the wiring from your house's electrical system and leave the remnants in the wall. However, you are obviously not allowed to leave any live wires just dangling there. You also aren't allowed to hide any junctions behind drywall etc. eg you can't just put wire nuts on the wires providing power to the switch and then drywall over the old box.