The prole woman singing behind Charrington's apartment is symbolic to Julia and Winston because she represents a "sort of melancholy" happiness. It would seem she was perfectly content with her lot in life, trudging on through the days, even if her days were full of endless lines of laundry. Winston muses that no member of the party would sing so "alone", "spontaneously" and thinks that it would be a "dangerous eccentricity" (148). The prole woman might be a Sisyphus of sorts, from the Myth of Sisyphus, constantly struggling against an isolated and alienated existence, or perhaps trying to be happy in a dire situation. She is an example of someone trying to make the best out of her situation in life.
The red-armed prole woman singing as she washes her family's clothes outside of Charrington's apartment symbolizes hope and represents a future after the Party is destroyed. After Winston is finished reading Goldstein's book, Orwell writes, "If there was hope, it lay in the proles!" (277). As Winston watches the prole woman singing to herself while she does her chores, it occurs to him that the proles will always survive. Despite the dire conditions and oppressive society that they live in, the proles will never go away. They account for 85% of the population and are strong, tough, emotional individuals. Although they are currently too ignorant to revolt against the authoritarian government, they will continue to live their lives freely. Winston has hope that one day the masses will be educated and united with one another to rise up. Therefore, the red-armed prole woman represents hope in a future void of absolute government control.
The singing prole represents a life style which Winston and Julia can only dream about. It is a lifestyle of such simplicity that the only thing one needs to worry about is the simple things like getting the clothes washed and dry. It also involves a family and love for their family. Being party members love is not allowed (which is why they have to be secret about it) and in the proles life there is a certain amount of strength in the sense that their lives aren't as controlled and they are capable of being more allowed to think as they wish.