Does copper wire go bad?

I was fixing a side marker on a 1972 Plymouth project car today. When I when to strip the old factory wire to make a connection, the wire came off along with the insulation, this happened two more times when I decided to use a razor blade instead of the wire strippers. It seems the copper wire all the way up, even though it is still covered in factory insulation, somehow got weak and fragile. What gives? Does the copper wire have a life expectancy of some kind? Oh, as a side note, I found with my digital voltmeter showed that both rear side marker wires were only reading 10 volts at the bulb socket (with the motor off). I wonder why it's not reading 12 volts? Thank you.