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As for a specific event, there is nothing specific to a text area. If you are cutting and pasting, you could maybe listen for the keyup event and see if it was a CTRL+V, but that wouldn't catch cases where you select Edit > Paste in the browser menu.
Side note, I've never seen any behavior like what you describe.
Although if there are multiple events being fired then it may get called more than once per paste so you might have to do some checking to see what is happening.