So... is Binbou Shimai Monogatari finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 15, 2006
Manga finished: October 19, 2006
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Binbou Shimai Monogatari centers on the lives of two sisters, Kyou and Asu, who are orphans navigating life without their parents.
The story follows their daily struggles as they cope with poverty, manage their household, and pursue their education.
Kyou, the older sister, works tirelessly at multiple part-time jobs to provide for herself and Asu.
Despite their hardships, the sisters are surrounded by supportive neighbors and friends, and their unbreakable bond helps them face any challenges that come their way.
The anime focuses on their resilience, the importance of family, and the small joys they find amidst their difficult circumstances.