A break in the filament of an electric bulb means:
a break in the path of the current between the terminals of the cell
An incomplete electric circuit
the bulb is fused
A break in the filament means that the bulb is fused. In this state if it is connected to any circuit then it would cause a break in the path of the current, as the charge carriers do not get a closed path, i.e. it will leave the electric circuit incomplete.