The fuse wire is always connected with the live wire of the circuit because when the fuse wire breaks in reaction to very high current, it breaks the circuit and brings it to zero potential.
If the fuse is instead added to the neutral wire, then too the fuse will break the circuit due to high current, but the appliance remains connected to the high current source through the live wire.
Therefore, a person touching the appliance may still receive a shock when they come in contact with the live wire, through the appliance.