Can the (cut) wiring be repaired on headphones?

The loose coppers wires can be twisted together they are the negative wire to your speakers, the fibers are just insulator & can be cut away. The red & green wires are the positive input to each speaker. You should have a negative wire & one of the positive wires going to each speaker they are actually ran around the outside of the positive (red & green) wires, if you trim back enough wire covering you should be able to tell which un-insulated copper ground goes to each speaker. The loose coppers wires can be twisted together they are the negative wire to your speakers, the fibers are just insulator & can be cut away. The red & green wires are the positive input to each speaker. You should have a negative wire & one of the positive wires going to each speaker they are actually ran around the outside of the positive (red & green) wires, if you trim back enough wire covering you should be able to tell which un-insulated copper ground goes to each speaker.

correct on the colours etc. but you cant simply twist the wires together because they are laminated copper, there is a coating (like a varnish) which acts as insulation. The best way to deal with that is by soldering, keep the soldering iron tip (with small blob of solder on it) applied to the wires for a few seconds and the coating simply burns off leaving a soldered wire ready for joining. Its a very fiddly job, but its feasible. correct on the colours etc. but you cant simply twist the wires together because they are laminated copper, there is a coating (like a varnish) which acts as insulation. The best way to deal with that is by soldering, keep the soldering iron tip (with small blob of solder on it) applied to the wires for a few seconds and the coating simply burns off leaving a soldered wire ready for joining. Its a very fiddly job, but its feasible.