SIDS, or sudden infant death syndrome, is quite rare, but it’s still a worry for many parents, especially if you have a preemie. Some monitors detect breathing and movement, but they cannot prevent SIDS. There is no link between short periods of apnea (not breathing) and SIDS (source).
Experts recommend you place your baby to sleep on their back and have a firm mattress. Parents often hate how firm their baby’s mattress is, but there is a safety reason for that (source).