Somewhere in the middle of a run - I'd cut, trim back and splice in a new bit of wire. Solder or crimp connectors, cover with shrink tubing.
If not any broken or corroded strands and you can get shrink tubing to the area (possibly by temporarily remove contacts elements from connecotr block as per below) the shrink tubing should be enough. Maybe two layers for even more wear resistance.
By a connector? - I'd cut it, trim back and splice in anew bit as per above, but on the connector side I'd remove the contact element from the block. Usually by pushing down one or more very small tabs that are part of the metal contact element. Can usually be gotten to from the 'face' of the connector using something very slim and stiff (smallest screwdriver in a jewelers screwdriver kit, sturdy sewing needle, ~0,5mm piano wire, etc) insert from the face side to push down the tab and extract the contact element to the back of the connector. Best to find the same crimp connector and press on a new to the spliced in wire and push into the block. Worst case, solder the wire to the used connector, carefully pry up the tab again and push back into the block.
In the image below you can see one tab on each of the contact elements,, and how it can be depressed by sliding in something from (in this pics orientation) above, going up the slope pushing the tab back down level with the rest of the connector. (from____/ ___ to ________)