This can be explained as a fuse is a protective device which blows in order to protect the circuit and the equipment from short circuiting.
Short circuit is a condition where a very heavy current flow through the line with no low line impedance which is not the intended path for the current to flow.
Thus when heavy current flows through a fuse it blows out thus disconnecting the path for the current flow.
Therefore, if a fuse burns out when switch is on, short circuit is present after the switch
