can you eat too few calories?

So I've seen a few studies that say there are different "zones" that your body is in depending on how much and what you eat.
One was a fat burning zone and the other was a storage zone. The storage zone was from not eating enough and causing the body to go into storing all the fat because it wasn't sure when it would get food again.

So here's my question (s), How do you know if your eating too few calories? : Is it just that you stop loosing weight? Do you just feel tired?, Is this really true? I know you are supposed to compare how active you are with your calorie intake but how much of a calorie deficit is too much? Would this deficit be different everyone?

I know there are other health problem associated with under nourishment (hair loss, eating disorders, etc), I'm not talking about those extremes. This is more to do with an obese person who actually needs to loose weight, not someone who is just trying to loose a couple vanity pounds that doesn't really need to, or shouldn't.

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