Regarding the second claim, wearing a bra will not help with breast sagging; this is caused by age, genetics, or pregnancy and breastfeeding. You should wear size-appropriate bra, with soft cups and without many wires and fasteners. This will give the support to the breast from sagging. Don`t buy smaller size and wear it in bed, the only “benefit” will be the discomfort.
Scientists have busted both myths: wearing a bra during your sleep won`t prevent sagging, and not wearing a bra won`t have any effect on the risk of breast cancer. It`s your choice either way. If you have sensitive breast, the bra will give you some support. If you have night sweats or sensitive skin, don`t wear a bra, it will make you more uncomfortable.
Whatever choice you make, don`t forget to choose a bra made from natural fiber, with soft cups and well-fitted so that you can wear it while sleeping and give you the needed support.