Just to clarify, this initial assumption is wrong.
When the copper wire (insulated) that forms the coil of an electromagnetic brake disappears at some point the electricity goes out of the way.
The wire doesn't go away or disappear. It is still in there causing a problem. The very thin lacquer insulation around the wire melts, or cracks, or burns,(goes away) allowing one turn of wire to directly contact a different turn where they were previously separated by the insulation. The electricity now mostly takes the shorter direct path. Does not circle around the core as many times. This reduces the electromagnet strength. Because the path is shorter, resistance is less, current increases, causing more insulation to fail, causing even less magnetism and resistance, and more current. At some point the brakes stop working either because the magnet is too weak(coil has continuity), or because the heat from high current has caused a solder joint, or an actual wire to break(coil has no continuity). A failed brake may not have a bad coil at all. The mechanical parts can fail or be contaminated by oil or grit.
If you wanted to "fix" the wire, you technically could unspool it, somehow strip off the failed lacquer, then reapply a fresh coat by threading it slowly through a bath of the stuff and air drying. This won't actually work because there are so many points of failure, but possible in theory.
If you wanted to respool the coil as BM said you will need to buy new lacquered wire to match the wire cross sectional area, insulation thickness, and length of the original. Then wind it to the same number of turns. You did remember to count the turns while unspooling, right? If the insulation is too thick(if you use regular wire) you get too few turns and too many layers. Weak magnet. If you use different cross section(gauge) or length of wire the resistance is different, so the current is different, so the magnet strength is different.
When buying this wire it will be called "enameled magnet wire".
https://www.remingtonindustries.com/magnet-wire/Or you can buy a complete replacement brake for about the same price and a lot less labor.
