"Zan Sayonara Zetsubō Sensei Bangai-chi" is a continuation of the "Sayonara Zetsubō Sensei" series, which revolves around the eccentric and perpetually pessimistic high school teacher Nozomu Itoshiki and his interactions with his equally peculiar students. The series maintains its signature satirical and absurdist humor, blending dark comedy with social commentary. Each episode is structured as a series of vignettes, often exploring themes of modern society, human behavior, and existential despair through exaggerated and surreal scenarios.

Nozomu Itoshiki, whose name can be read as "despair" when written vertically, is the central figure, embodying a nihilistic worldview. His students, each representing a specific archetype or societal critique, include characters like Kafuka Fuura, an overly optimistic girl who contrasts sharply with Itoshiki's pessimism; Abiru Kobushi, a transfer student with a mysterious past; and Chiri Kitsu, a perfectionist with obsessive tendencies. The dynamic between Itoshiki and his students drives much of the narrative, with their interactions often escalating into absurd and comedic situations.

The plot does not follow a linear storyline but instead presents a series of loosely connected skits and parodies. These segments frequently reference Japanese culture, pop media, and contemporary issues, often breaking the fourth wall or employing meta-humor. The series also incorporates visual gags, wordplay, and rapid-fire dialogue, requiring familiarity with Japanese language and culture to fully appreciate its nuances.

"Zan Sayonara Zetsubō Sensei Bangai-chi" serves as a supplementary installment, offering additional episodes and content that expand on the themes and characters established in the main series. It retains the same stylistic approach, with minimalist animation and a focus on dialogue-driven humor. The series continues to explore the absurdities of life through the lens of Itoshiki's despair, providing a unique blend of comedy and introspection.