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
All of these
A break in the filament means that the bulb is fused. In this state, if it is connected to a battery, current will not flow as the charge carriers do not get a closed path, i.e. the electric circuit is incomplete.
Since there is no current through the filament the bulb will not glow.