Per <R.15.a.ii> in the VEX game manual, external motor wires may be repaired. There are a number of ways to repair broken wires; the most common wire failure is broken connector pins. These can be repaired by:
Internal repairs are possible, but the legality is questionable. However, so long as the original functionality and capabilities of the motor are maintained, and any overload mechanisms are not removed, it would be very difficult to distinguish between a well-done internal repair and an untouched motor. To be safe and to ensure not running afoul of any rules, any internally repaired motors should not be used for competition.