How should a radio receiver be used to detect damage to concealed wiring?
Cotton braiding will not be doing anything useful RF-wise (attenuation or modification) that means you could determine its presence or not or general condition. A broken or short-circuited copper core may give off some detectable signal, but that's not your question.

A simple oscilloscope-based Time Domain reflectometer could help tracing faulty cables, but they only really show breaks, shorts, changes of impedance, etc. and on short runs (&lt;100m) you need relatively fast/expensive measurement.

In your situation, an undesirable bare copper wire touching bare dry wood will likely not be detected. If the wood was damp (hence conductive), or the wire was touching a nail or similar, then it's possible you might pick it up, but you'd need a pretty sensitive setup.

Basic TDR's are DIY-able with a simple pulse-generator circuit and any oscilloscope, but results may vary greatly. They're used commercially in telecomms on both copper &amp; fibre-optics to qualify &amp; fault-locate cables and the good ones are really great bits of kit. Due to the speed of light/electrons, short cables present quite a challenge.