I think it's called the Peter Principle when you are promoted to a position of incompetence.
An interesting question is if the incompetence causes the corruption because they just don't know what to do so they just say, "Fuck it." It could even work vice versa but that would require some extra stuff to happen (such as corruption leading to being in a position of incompetence, like cheating to get a job or something).
Either of those are possibilities ;o
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