Is it possible that if you have a baby, you could die when the baby is born?

It is possible. Rate of maternal mortality varries greatly from 1:100 in mozambique to < 10:100, 000 in usa and a few other countries. The mother's general health issues and pregnancy-specific complications such as placental issues and preeclampsia increase the risk of maternal mortality. Risk of death is not only during child birth but also at anytime during pregnancy.