Can a baby born in 44 weeks?

I'm guessing that you mean at 44weeks gestation - i.e. a month 'overdue'. While it's not common for caregivers to be comfortable witha woman continuing beyond 41-42 weeks gestation, due to fears of the placenta becoming less efficient and potentially compromising baby's well-being, it is a woman's choice whether to be medically induced or not. There are certainly historical cases of woman carrying babies well beyond their due dates. Another thing to consider is whether the woman's normal menstrual cycle is particularly long (the average is 28 days) - if so this will have affected the conception date, and therefore while her official due date calculated by her last period may in fact be a couple of weeks out... so that 44 week baby may in fact be right on time! This is particularly relevant if the woman chose not to have an ultrasoun scan during the pregnancy, which provides information on dating the pregnancy.
Good luck!