Yes it happened me. My daughter was only 5lbs at 36 weeks and she did not grow since 34 weeks. My OB was worried it would cause problem to my baby. So, she suggested to have an induction at 37 weeks. Before I reached 37 weeks, I was at Civic for an ultrasound appointment and ended up giving birth to my daughter unexpectedly. She was born varginally at 36 weeks + 3 days at 5lbs 1 oz. She was healthy and just passed 5 lbs so she did not have to stay in the incubator but she had jaundice 3 days after birth. She was at CHEO doing phototherapy for 5 days. Now, she is 1 year old, very healthy and active. I hope my experience would make you feel better. Dont worry, you should trust your OB. Hope everything would go well. Good luck!