Which wire are you talking about?
The wire cable that goes to the clamp that pulls the plug out of the switch or the wire(s) that go the the
electrical part of the switch?
Basically the pull wire if the activation plug is not pulled out there would be no effect.
If the activating plug has pulled out then that would put 12 volts on the brake coils, locking up the
brakes electrically. This would be a big issue.
If a wire is pulled from the switch then either it is the +12 volt from the
battery and could short and blow the fuse (no affect on the brakes, or it is the wire from the switch to the brake coils and if it is broken again no effect to regular braking.
So it depends on what wire.
Unless the brakes are being applied by the switch activated by the plug being pulled and putting the brakes on and wearing and overheating them, probably sliding the
tires this would no cause brake grabbing on it's own.