These and other high-altitude balloons are almost never tethered nor recovered - they're not a kite, that would be completely impractical.

You're nearing the altitudes at which the tensile strength of even supermaterials like Dyneema fibers are unable to lift the weight of their own tail, much less hold up against the tension of the jet stream. You'd need some kind of reverse rocket equation pyramid, where the topmost thousand meters have to lift the entire line, and are therefore made from line 0.6mm in diameter, and the next thousand meters are made of a slightly thinner, slightly less strong, slightly lighter fiber (because they don't have to lift the top thousand meters of line), and so on for the next 50-100km, depending on how much sag you expect the line to have.

"Oops, the balloon popped, excuse me while I do an ultramarathon across town spooling up my thousand-dollar tether from everyone's backyards...please don't cut it or trip over it or drive over it..."

No, it merely trails a 5 meter length of wire that acts as an antenna. You can receive the signals from hundreds of amateur receivers set up across the globe, often receiving transmissions at very long ranges. When the balloon eventually falls, yes, it's litter, but it's only a couple grams - go to your local park and pick up some trash, you can atone for a lifetime of HAB hobby sins with a single black bag full of alcohol bottles, fast food wrappers, and cigarette buts.

> almost never tethered

yet you can't say never, hence the question. balloons are launched for different purposes. if you're trying to keep a balloon on station to gather local data, it's gotta be tethered. maybe not typical of a 40k' altitude, but they definitely use tethered balloons.