Pretty much all chevy spare tire hoists are like this. Most other vehicles will have a similar design. It's not the cable that freezes. The spare tire anchor has a safety latch that freezes in place. The tire will come down a few inches then stop. Keep turning the handle and the cable will come down but not the tire.
Do not spray them with lube until you manage to get them down! Lube will only gum up the rust. Keep it dry so you can shake and scrape away the rust. Once it's down and you can work it back and forth... THAT'S when you want to spray it!
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