Antique sheets, tablecloths and clothes are a treasure to have and use, but storing them takes treatment. They shouldn’t be put on hangers or folded, as the fabric weakens along the folds and is stressed by hanging.
Find a cardboard tube to roll them around and store them safely that way. If you have a very large item, such as a quilt, which has to be folded, use acid-free tissue paper between each fold to prevent creasing.