Does copper wire go bad?

There are a few things that can happen. Copper work hardens, the more it is bent, the more brittle it becomes. Corrosion from salt, and other contaminants also damage copper. Nicks in the copper will also result in strand breakage, best to use correct wire strippers, that only cut insulation, and not nick the copper.
The low voltage readings, may result of poor connections in the harness. Best to find a factory service manual, and find all connection points. Housing grounds important too.