If you're thinking of a word that sounds like "flump" and means to fall heavily, then you might be thinking of "plump" or "flop."
Here are some examples:
* Plump: The cat plumped down on the cushion with a satisfied sigh.
* Flop: The tired dog flopped down on the floor beside me.
Can you tell me more about the context you were thinking of? I might be able to help you find the right word.