TVtropes defines it as
The desire to end a story on An Aesop is natural and strong: it's often the only thing that elevates the story above a piece of insubstantial fluff. The trouble is that it doesn't always work. And when there's Executive Meddling or a Writer On Board, the moral of the story feels as awkwardly tacked-on as the spoof "Wheel of Morality" lessons that ended many Animaniacs episodes.
Basically, a Broken Aesop is a story where the moral at the end of the episode doesn't match the moral that the episode actually contained (and unlike the Spoof Aesop, they don't do it on purpose). It's an Anvil Ex Machina.
Common methods of breaking An Aesop include:
- A Reset Button or Snap Back: There's a lesson, but because next episode will pretend it didn't happen, there are no consequences.
- Have the resolution rely on a Deus Ex Machina, Fantastic Aesop, or Twilight Zone Twist.
- Distorting the moral into "It's only wrong if you do it."
- Making a character behave in an uncharacteristic manner or break with series continuity to teach the moral.
- Trying to present a moral ambiguity and failing badly.
- Trying to teach Be Careful What You Wish For by using a Literal or Jackass Genie who doesn't actually give you what you wished for.
- Miscommunicating with the audience, such as where the audience reads a character differently than the author did.