In an extreme situation, the barrel could become too thin. I've never head of this happening from normal wear. The closest things, I'm aware of, are: When a screw-in choke is improperly installed and the end separates; someone tries to extend a chamber (or overbore) when there's not enough material (both are the result of poor gunsmithing); or corrosion damage.
Taking barrel measurements won't tell you much unless you know the properties of the specific steel alloy used. Higher strength steels allow thinner barrels. If a gun passes a visual inspection and you're still in doubt, consider proof testing.