Not too long ago I purchase a used Apple Cinema display, A1267, 24". It worked fine out of the box, but it was disconnected for a while, then moved to a different room. It would then not turn on, but the power to the laptop and the iSight camera both worked (there are reports of the USB ports working and not working). The problem it seems is the thin ground shield foil inside the all-in-one cable gets broken. This solution is based mostly on a reply to fevangelou (https://forums.macrumors.com/members/fevangelou.953692/) by Mac_Dino in 2018, on MacRumors, but embellished some. Cut 1" wide lengths of aluminum or tin foil, and wrap around the all-in-one cable from the Display Port plug to the back of the monitor, make sure at each joint in the foil is 1" or more overlapped. Take some thin bare wire (I used wire wrap wire, AWG 28, about 3", and wrap around outer metal ground shield of the Display port plug and then around the aluminum/tin foil at the display port plug. Plug in the display port plug and power to the display. If it now works you might try a drop of solder on the wire to the ground shield of the display port connector, a drop or two between the wire to the foil there, and another wire connector/jumper from the shield to ground inside the display with drops of solder there too (I have not attempted this yet). Twist some more wire around each joint in the foil.
An acquaintance has one of these in the same situation, so I went looking around the internet for solutions. While I think what you describe may work for a while, I fear you’re hitting the age limit of the plastic that surrounds the cable, and it’s just going to fray again as the plastic becomes brittle elsewhere.
The better solution is to replace the cable, but they aren’t cheap: $100 to $150 US.
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my cable seems pretty flexible to me. It’s not plastic, it’s rubber.
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Where did you find them? The forum I was looking at, and referred to was from 2018 and at that time they said they were not available, only source was eBay, and those would have the same age problem.
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$150 is close to what I paid for the monitor.
The Apple part number is 922-8679. Here are a couple of places I found that carry it. I have no affiliation with these places, nor have I ordered from them, so buyer beware:
Just due the fact Apple has not made these for years, the chance of one of these working for a while is slim. As I think I said, it is the foil shield in the cable that breaks so the cable no longer works. I can see that foil shield, as I have worked with it several times, as breaking anytime you move the cable. So wrapping it up to ship is possible time for it to break.