can a cat get sick from a flea collar?

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YES, THEY CAN BECOME VERY ILL FROM CERTAIN FLEA COLLARS!    Additionally, Flea collars are relatively ineffective as they only control a few inches around the collar and can cause allergic reactions on the pet.  Most sprays are also short lasting and kill only adult fleas. 
More effective treatments that are available are the topical products applied on the pet’s back.  These products last longer and continually kill adult fleas.  However, all of these products are not the same and there are major differences in their effectiveness.  The over the counter topical products that have various trade names are usually permethrin-based and must be very concentrated for effective flea control.  Some also contain growth regulators to inhibit flea eggs. 
Permethrin products should not be used on cats as they are very toxic and we see several toxicities every year when these products are applied to cats.  Even cats lying next to dogs can become toxic.  Also, these products are not waterproof so bathing or just swimming in a farm pond will wash them off the coat.  Permethrin has been around for over 20 years and there is considerable documented resistance in many flea populations, and most of these products last closer to 2 weeks than the reported 4 weeks. 
Over the counter flea control products for topical use on dogs and cats are mostly permethrin-based, and should never be used on cats, are not water proof, and can be washed off with bathing or swimming.  More effective products available only from your veterinarian include Advantage, Frontline, and Revolution. 
Advantage is a topical product for flea control on dogs over 7 weeks of age and cats over 8 weeks of age that kills all adult fleas within 24 hours and lasts for a month.  It is waterproof for swimming and bathing as long as a soap free shampoo is used no more than every 2 weeks.  K-9 Advantix is a new product that contains the same ingredient for flea control as Advantage plus a permethrin for tick control.  Frontline is also a topical product for dogs over 10 weeks and cats over 12 weeks of age.  This product is concentrated in the sebaceous glands of the pet’s skin and will not be removed with bathing or swimming.  Frontline kills all adult fleas within 42 hours and lasts 1 month, and is also effective for tick control.  A newer product, Frontline Plus, also has an insect growth regulator to prevent flea eggs from developing in to larvae.  Because Frontline spreads in the oils on the coat, it should not be applied within 2 days of bathing.  Revolution, another topical flea product, can be used on dogs and cats over 6 weeks of age, and also has activity against heartworms, ear mites, sarcoptic mange in dogs, roundworms and hookworms in cats, and some tick control in dogs.  Revolution is waterproof as it is absorbed into the animal’s body.  Capstar is a tablet available from your vet that kills 90% of the fleas within 4 hours and is useful in cases with a heavy infestation of adult fleas, but has no residual activity.  One of the most effective tick control products is a Preventic collar, which also has a flea growth regulator in the collar.  Consult with your veterinarian to find out which products they recommend for your pet!