Because the widow is alone and Young Fu is her only son, he is allowed to complete his apprenticeship while living in a small rented room with her, rather than living in the shop, a plot device which allows us to see more of the city than might otherwise be the case.
Since the widow is alone and Young Fu is her only son, he can continue his apprenticeship at home in a modest rented room instead of working in the shop. This arrangement allows for greater exploration of the city's sights and sounds.