A lot of women ask this question because they’ve been told to never sleep on their backs, particularly in the third trimester. Most advice on the Internet and in books about pregnancy recommends against sleeping on your back. There is no good scientific evidence that sleeping on the back increases the risk of stillbirth, even in the third trimester. There have been studies that show that fetuses have some fetal heart rate changes in different sleep patterns while the mother is sleeping on her back, but these changes have not been definitively associated with an increased risk of stillbirth. Studies of observed sleeping habits show that women roll around a lot and likely have little control how they lie during sleep.
Women in the third trimester are unlikely to sleep on their backs naturally due to their belly size, so they will tend to sleep on one side or the other anyway. If they do sleep on their backs, there is little to do about it since women have no control over how they turn and roll during sleep. Since there has been no definitive connection between back sleeping and stillbirth, women should not lose too much sleep (pun intended) worrying about how they sleep.