I'm sorry to hear Molly is always cleaning herself and has you worried because she's losing her fur. This sounds like an OCD condition called feline psychogenic alopecia. Here is more information:
There can be many causes for this condition, but main ones are stress, boredom, allergies and external parasites like fleas or mites. Even if Molly is an indoor-only cat, she cans still be affected by fleas, brought in by humans on shoes and clothing. However, food allergies may also cause the constant grooming, if her skin is itchy.
Typically, the most common cause for this condition is stress or anxiety, even though she may not seem stressed to you--cats show their stress through certain behavior patterns that are usually different than humans.
It would be best to bring Molly in for an in-person evaluation by her vet and have a skin scraping (painless), to see if there are any microscopic parasites or eggs and also, to rule out any food allergies. If her current food includes corn, wheat, gluten, soy, carrageenan, artificial flavors, colors and/or preservatives, these are common allergens for cats. Also, feeding grain-free is considered the healthiest. Here is a series of articles written by a feline vet on the best way to feed our cats:
If everything else is well, medically (hopefully), the vet may prescribe an anti-anxiety medication that will help her stop this behavior.
You can also try Feliway plug-in diffusers, which emit cat-calming pheromones and have no scent to humans. Here is additional information:
I hope all will be well with Molly!
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