Augean
Etymology
From the stables of King Augeas in Greek myth, which housed thousands of cattle and had gone uncleaned for thirty years. As one of his Twelve Labors, Heracles cleaned them in a single day by diverting two rivers to flush them out. The adjective names both extreme filth and the heroic scale of effort needed to remedy it.
adjective · /aw-JEE-un/
Extremely filthy or corrupt, or requiring an immense effort of cleaning up or reform.
What it names
The accumulated squalor of long neglect — reach for it when a mess or a corrupt institution has festered so long that clearing it out is itself a monumental task.
Example
The new director faced an augean task: decades of unpaid fines, lost records, and quiet corruption to sweep out.
Related idea
Squalid simply describes dirty, degraded conditions; augean adds the sense of long accumulation and the near-impossible labor of setting things right.