So... is Human Bug Daigaku finished or not?
NO, it is not finished.
Why?
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Human Bug Daigaku centers on Satake Hirofumi, a death row inmate with an unusual characteristic: he's virtually unkillable.
This draws the attention of "Human Crazy University," an organization dedicated to studying extraordinary events and the people connected to them.
Satake becomes a subject of their research, sharing his past experiences of survival and his complicated life, including the circumstances surrounding his fiancée's murder.
As Satake's story unfolds, the university discovers that his actions may be tied to a much larger and more sinister conspiracy than anyone initially suspected. It's a journey into the depths of his seemingly immortal, yet troubled, existence.