Is it true that if you eat below 20 carbs a day your body will go into starvation mode and you wont lose any weight?

The only thing I know (have heard and believe) about the 20 carb limit is that if you eat 20 carbs or less it produces the same result. In other words if you limit yourself to 10 carbs you aren't doing your body any good because you would get the same results at 20.

Some input on this would be very helpful. I've been reading about it lately and am confused. If someone could point it out in the book also that would be great.