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The company example sounds like Tyrant Takes the Helm, like "Now that I'm in charge, we're going to do things the right way, by which I mean my personally favored way."
It also has shades of Vetinari Job Security. Leader goes absent, problems immediately start, and everyone who tries to backfill the leader position can't do it. Usually ends with everyone begging the original leader to return (assuming they return from a temporary absence or un-retire).
A situation where The Leader is absent, and the one who takes charge in their place leads differently (according to their own idea of what's good for the team), which usually leads to problems.
For example, the CEO of a tech company gets sick/arrested/dies, so one of the department heads is given temporary CEO powers to avoid a Too Many Cooks situation. The problem is they start running the company as though it were their department: Marketing spends a lot more on advertising and less on quality, R&D pushes towards making Awesome, but Impractical(ly expensive) products, Accounting starts pinching pennies everywherer they can, Sales gets the company in legal trouble by making promises the company can't keep, HR and Legal focus on reducing company liability in any way they can, IT starts The Purge of those employees who need their password reset five times a day, etc.
In Animorphs, Rachel takes over the team for one book in Jake's absence. They start hitting the Yeerks harder and faster, befitting Rachel's Blood Knight tendencies, but also leads to them getting caught in a trap and Cassie nearly being infested.
Edited by Chabal2