Excessive fleas cause a condition called “Flea Anemia.”  It reduces the number of red blood cells and/or hemoglobin which can be deadly.  It is more prevalant in animals that are kept outdoors most of the time.  Thus, more cats die from this condition than dogs, but not exclusively.  For more detailed information or for a place to point a client with a pet with excessive fleas look here:
https://www.lakecityhumane.org/post/flea-anemia-more-than-just-a-nuisance