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Hi there and thanks for your question.
The pattern of hair loss that you have described does indeed sound like it is caused by stress. We don't really know why some cats do this, but some cats will obsessively overgroom when stressed. Often the source of stress is unknown, but having another cat in the house with which she does not get along can certainly cause it.
You may want to look into a product called Feliway. It is a little pricey but tends to work well to relieve stress. It comes either in a spray that you spray in the air or a plugin that diffuses the substance into the air regularly. It is a feline pheromone which is like "happy hormones" being released and it is totally safe.
Or, you may want to ask your vet about medicines to help to reduce the stress level.
There are other things that can cause hair loss such as allergies, fleas, ringworm, etc, but usually we see scabs, flakiness or itchiness and it doesn't sound like your cat has these.
I hope this information helps! If you have more questions regarding this problem, just hit reply. If I am online I will respond right away. Otherwise I will respond as soon as I come online again. Or, if my answer is sufficient, then please hit accept. Thanks!
The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would highly advise contacting your regular veterinarian.