Answer:
On melting of filament in the bulb, the circuit will break and hence will not be able to conduct electricity. Thus, the rest connected bulbs will not glow. Filament of bulbs are made of an alloy having high melting point, so that it remains undamaged on increase in temperature.
Because the bulbs are added in parallel, the resistance in the circuit from the bulbs is reduced increasing the current (flow of electrons) through the circuit. The filament heats up due to the increased amperage load that it is required to carry. Eventually it will oxidize and melt.
