Nothing will happen to your health if you eat garlic on an empty stomach.
It's actually recommended that if you're eating garlic for it's health benefits that you do eat the Garlic on an empty stomach before eating anything else.
Eating Raw Garlic on an empty stomach makes the Garlic work better as a natural antibiotic which can ward off heart disease and even cancer.
When your stomach is empty the bacteria is more exposed to the garlic and they will be killed off much quicker from the antibiotics that garlic naturally contains.