Yes, worms can kill kittens. A heavy infestation of ascarids (roundworms) can result in severe illness and possibly death. A hookworm infestation can be fatal in very young kittens.
In all, although some are rare, there are ten different types of parasitic worm which can infect a cat: roundworm, hookworm, tapeworm, roundworm (trichinosis), strongyloides, whipworms, flukes, stomach worms, heartworms, eye worms.
Roundworms are the most common worm parasite in cats. A large percentage of kittens are infected. Twenty-five to seventy-five percent of adult cats are infected with roundworms. They grow to 5 inches in length. Cats acquire roundworms by ingesting roundworm eggs perhaps by licking them off their paws when walking over contaminated soil or by eating a host creature such as a beetle of a rodent. Infected kittens are thin and pot bellied. They may cough, vomit, be anaemic and get pneumonia. The roundworm looks like alive spaghetti.
Hookworms are small and thin at .25 to .5 inches in length. They draw blood from the wall of the intestine. They are more common in dogs than cats. They are more prevalent in southern US states where it is hotter and more humid. Cats get hookworms by eating infected larvae in soil of feces or by direct penetration of the pads of the paws. Newborn kittens might get hookworms from their mother’s milk. Cats who recover can become carriers with cysts in the tissue. A new outbreak can occur.