I heard a baby can be born early and can die from periodontal disease?

Yes and No. A 2006 published study in the journal of american dental association showed a positive association demonstrated that pregnant women with periodontal disease are up to 7.5 times more likely to delivery of a preterm/low-birth-weight infant compare to pregnant women without periodontal disease. However, baby can not die from periodontal disease.
Possibly. The death would be from deficiency of coenzyme q10 that would be responsible for the dental disease. Any interference with energy metabolism is a risk factor and is the obvious reason for good diet and supplementary vitamins in pregnancy.
INFLAMMATION. Periodontal disease is an inflammatory process of the the gums. It is the most prevelant chronic disease in the world. Inflammation anywhere in the body it is unhealthy for the mother. This disease has been linked to heart disease, stroke, diabetes, certain cancers and yes, pre-term birth (born early). The baby is not born with the disease but it can effect the baby...Possible birth defects.
RARE RARE RARE. I am aware of one report: http://www.Nbcnews.Com/id/34979552/ however, if valid, this would be an extremely rare occurrence. Just another reason for everyone, especially pregnant women, to make sure they have a healthy mouth and seek routine dental care.
Not likely. Periodontal disease is usually established after the permanent teeth have erupted at a more mature age-20s or older. Juvenile gingivitis is very rare. Usually from my experience with twin premature daughters, it is hyalin membrane disease or immature lung or other organs that cause death. You may want to consult a neonatologist who takes care of premature babies for an answer.