Meaning:
(proverb) When someone loses power, their supporters or followers will
desert them. The phrase comes from a Chinese proverb.
Example:
I'm not surprised that so many board members are stepping down now that the
CEO has resigned in disgrace. When the tree falls, the monkeys scatter.
https://www.thefreedictionary.com [edited]
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Where I grew up, loyalty is highly valued and moral and it's the lack of it at
the worst time that the saying tries to convey. The monkeys owe the tree for
shelter and deserting it right at its downfall is cold. Of course, no one
expects them to be real troopers and there's little the landed simians could do
unless one of them happens to be the Monkey King.