BMI is not a fully agreed or understood measure, and it's not as simple as "you are healthy", "you are not". And it is most certainly NOT the case that people at the lower end of the BMI are healthier.
In fact, a recent piece of research published in the Journal of the American Medical Association suggests quite the opposite. The below quotes from an article about the research, not the research itself:
"Firstly, they found that obesity isn't as dangerous as it used to be. The risk of premature death as well as the overall mortality rate for obese individuals (with a BMI of 30 or above) is no longer higher than it is for normal weight (those with a BMI between 18.5 and 25) individuals...Secondly, they found the BMI that is currently associated with the lowest risk of death has increased from 23.7 in the 1970s to 27, which falls in the overweight category."
It is clarified that they're not trying to make people gain weight, and that obesity is not a healthy place to be, but they also say
"Overall, we should shift away from crude numbers as the sole measure of health but take into account dynamic measures like exercise tolerance, total body fat percentage, and other bio markers collectively to assess health," says Sonpal. "BMI is just one component of the overall global health index."
Shape also plays a part in it - with the classic pear shape able to carry a lot more weight without affecting health than the apple, which could imply greater levels of visceral fat.
Weight loss is also not as simple as calories in, calories out, and if you've been naturally thin all your life, you may not be very healthy at all and you don't necessarily deserve any credit for that achievement. Some of my skinniest friends eat horrendously because they don't need to worry about their weight.
OP - please don't starve yourself - you're more likely to fall off the wagon if you do. If you're thinking about keeping to that low level of daily calories (virtually a Very Low Calorie Diet - VLCD), you may be better off doing something like Exante meal replacements, which provides all the nutrients you need, plus protein to keep you feeling full. Slimming World is a slower approach, but it's an effective healthy eating plan for life that encourages lots of fruit and veg, lean meats and complex carbs as well as exercise. (I have no affiliation with either). Be safe and look after yourself.
Source:
www.shape.com/weight-loss/management/healthiest-bmi-actually-overweight-says-new-study