Pastel paintings created with artist's quality pastels on acid-free grounds are very stable. The dry colors are applied directly to the ground which is an acid free paper with either a rough texture or a coating containing pumice that grips the pastel. When I complete a painting I give it a couple of thumps on the back to remove any loose pastel dust then frame it behind glass or acrylic to protect the surface.
Properly framed pastels are very sturdy, long-lived paintings.
Some things to remember:
Avoid hanging any art in direct sunlight.
When transporting a pastel painting, keep the painting face up and avoid sharp jarring.
Do not spray cleaners directly on glass or frame - moisture can seep under the glass and cause damage.