Is it possible for a woman to be pregnant for longer than 9 months and not give birth because the baby died and she didn't know?

Very unlikely: A stillbirth is a tragic affair, any way it's viewed. However, it is highly unlikely for the body to keep a child that has died. Usually after the death of the baby, the body will attempt to expel it, usually starting labor or breaking down the fetus and expelling it over time. Generally an OB will note that there is no heart rate on visits and do an ultrasound to check.