I was at the new city hall building in Portland and the main elevator's governor rope had a weird, braided nylon sheath I've never seen before. | Elevator Mechanics - The Community Guide
You mentioned the governor rope, but that's actually the traveling cable for the car. The governor rope is a separate, smaller cable that runs in its own sheathing. What you saw is probably just a newer type of jacket material on the traveling cables, some of them are switching to synthetic.
Yeah the jacket material thing @richard_kelly54 mentioned tracks. Saw a building last year where the traveling cables looked totally different, almost like a thick plastic coating. Threw me off at first. Supervisor said it was some new polymer blend, supposed to last longer.