No, on my mis-installed cable, there's a tubular compression clamp that joins the ends. It's like a butt connector for wiring. I guess that way the whole loop could pass through a wide pully, but that's not an issue here. I don't know whether or not there's a special tool for compressing the clamp round or even if you need it, since the join will spend its life at the back of the seat.
One thing I think I missed the first time was that this is a stranded cable, either stainless or galvanized.
You used to see it used in olden days, before automatic dryers, for clothes lines on the second story of houses. I used to wonder what would happen to Mom's drying laundry if the line ever broke reeling it in or out, but it never did.