Hi,
Usually a MOV is connected in parallel to your application.
On overvoltage it becomes conductive...if it fails it should become low impedance causing a short circuit.
If you then apply power to your circuit..overcurrent may occur.
To avoid damage (wires, connectors, PCB traces) you should use a fuse in series to the application.
The fuse trips and disconnects the application from power.
But if you omit the fuse and don't have any other current limiter installed then I expect this will cause damage to wires, connectors, PCB traces...
It depends on where the damage happens whether your application is protected or not.
It's a problem of correct design.
I assume the datashett of the MOV, or application notes from the MOV manufacturer will show you how to correctly design a protection circuit.
Klaus