Now there is a permanent crease running through its middle. Hmm, not unlike the museum's director. If you must fold the piece, plan on changing the fold's position every few months. For flat pieces such as rugs, samplers or whatever, carefully and loosely roll them on acid- free tubes, and cover them with plastic. Leave the ends of the plastic open so air can circulate throughout the piece.
Light can be very damaging to textiles on two counts.
First, the fibers of some materials, such as silk, weaken when exposed to sunlight. Second, the dyes used in the patterns will fade in light. This is especially true with framed pieces because the glass can focus the light in a certain spot and act just like a magnifying glass, and the hot air in the closed frame will bake your grandmother's crocheting. The safest thing to do is store or display textiles in an area of reduced or indirect light. Speaking of displaying textiles, don't nail or tack material to a wood strip.