Cat flea photographic set up
Cat fleas actually infest a range of mammals, including dogs, racoons, sheep and many others. The adults live amongst the fur, feeding on blood. The eggs fall out of the cat and, those dropping on the animal usual sleeping places tend to be the ones developing successfully, and they are warmer and have the right humidity, as the larvae are very sensitive to cold temperatures and dry conditions. As for their food, they eat flea droppings, which are protein rich and contain only partially digested blood, so you could see this as a form of parental care, the parents providing food for the developing larvae in the form of droppings, which accumulate where the cat sleeps.
Rust, M. K., & Dryden, M. W. (1997). The biology, ecology, and management of the cat flea. Annual review of entomology, 42(1), 451-473. here.