Filament breakage in light bulbs is most likely to occur during the on/off cycling due to significant temperature changes that create maximum stress on the filament. The discussion highlights that bulbs often burn out when turned on, as the sudden temperature shift can lead to concentrated thermal stresses. Participants express interest in the underlying mechanics, suggesting that viscoplasticity and non-homogeneous temperature distribution also contribute to filament failure. The consensus indicates that deformation plays a critical role in the durability of the filament. Understanding these factors can help in mitigating filament breakage in light bulbs.