My CNC router at the program for mentally-handicapped people have steper motors similar to the one shown in the image. Can wires inside the motors go bad? HobbyUnlimited Nema 34 Stepper Motor 6A 8.5Nm (1200 oz-in) 118mm Length for CNC Router Mill Lathe, Black - Amazon.com
Theoretically, anything can happen. But usually more likely wiring itself New CNC controller board? Test by swapping wiring, if issue persists - replace motor
My experience with motors is with much larger (150 horsepower) motors, but any motor can fail internally. The most common failure is breakdown of the insulation on the windings resulting in a phase-to-phase or phase-to-ground short. When this happens on large motors the result can be the sudden ejection of pounds of molten copper and plasma. For NEMA 34 motors you would see either rough running or not running at all. You can check the winding resistance and resistance to ground on the motor for a more detailed analysis, but the easiest way for a quick test is to swap the motor with one that's working. If the problem follows the motor the issue is with the motor. Otherwise, it's somewhere else. But first I would visually check the wiring between the motor and the controller, especially the connectors and any point that flexes when the machine is moving. Or you could check continuity of the wiring with an ohm meter if you have one.
I would lump those as part of the wiring from the motor to the controller. The most likely reason for those to fail is physical damage - either they get cut or pinched somewhere, or there's failure where the wires are attached to the connector caused by flex.
I think that the problems are caused by the green terminal blocks that plug into the drivers. The wires can come off the terminals if they are not tightened properly or if the wires are not inserted properly into the terminals.