It's not just the nylon covering on THHN/THWN, we learned, but the sheaths on cable assemblies also often are optional. A cable installer nicked the sheath of a nonmetallic cable installed in a dry indoor location, and responded in a curious way: he turned the cable so the nick faced toward the wall. Not a bad response, Dave opined (while not wholeheartedly endorsing); this way, people glancing at it in passing wouldn't be unnecessarily concerned.
You may detect from this that Dave is quite an engaging speaker; moreover he's one with 19 years' product and Code experience under his belt to give plenty of clout to the information.
Damage is not necessarily limited solely to cable sheaths, of course. If a cable appears damaged, Dave recommends cutting a window in the sheath so you can examine the conductor insulation beneath. If that's good, you can "reinstall the window."
What should you do when you do want to, or need to, repair a cable sheath? Vinyl tape does just fine, Dave said, except in a wet location, and self-sealing mastic tape does even better. Best is a layer of self-fusing tape covered by a layer of vinyl. It even can be used outdoors on UF or SE cable, so long as it is not buried. For that, you need the sealing coverings that come with a Listed underground splice kit.
Art asked whether NM or SE cable repaired in this way still meets the UL standard. Dave commented that it is tough to say. There needs to be a dialogue between the manufacturer, AHJ, and installer. A qualified installer of repair materials should be able to make a repair acceptable to the AHJ, and Southwire's warranty will remain in effect.