During a leakage, the load will be by-passed. Current from the "live" wire will flow to the "earth" wire direct. This produces a large currentbe cause both the "live" and "earth" wires are of very low resistance. Such large current will blow the fuse instantly.
After the fuse is blown, the "live" wire is broken and no longer connected to the appliance. There would not be any current in it. This avoids the danger of electric shock.