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Cats can NOT go without eating. The longer (usually over three days) they go, the more chances of hepatic lipidosis, or liver damage and failure.
This cat NEEDS to be seen by a vet as soon as possible, if she does not want to lose the cat.
It may have diabetes, or hyperthyroidism, or any other number of things, but not eating this long, with that kind of weight loss, if very serious in a cat.
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God bless and good luck!