There are two common faults with field coils
Shorting occurs when one turn connects to another within the field coil caused by a breakdown of the insulation on the wire between the turns.
When this happens it causes a large current to flow within the shorted turn. The heat generated by this can cause the field coil to heat up and burn out, or for the wire to melt and break the circuit - stopping the current flow through it.
The second major fault is earthing. This usually occurs when the taping around the coil degrades and wire from within the field coil comes into contact with the metal body of the unit.
This causes the electrical supply to the field coil to prematurely find its way to ground, or negative.