Most fabrics degrade with washing. Linen is one of the few that improves, and it's worth understanding why, because it changes how you think about a "worn-in" piece.
New linen fibers have a naturally stiff structure held together partly by pectin, a plant compound left over from processing. Each wash and dry cycle breaks down a small amount of that pectin and relaxes the weave slightly, which is what produces the soft, broken-in hand of well-used linen.
This is different from cotton softening, which often comes from fibers physically wearing down and weakening. Linen's individual fibers are stronger than cotton's to begin with, so the softening process doesn't come at the same durability cost, a well-made linen piece can go through hundreds of wash cycles and still hold its structure.
Practically, this means a linen piece that feels slightly crisp on arrival isn't a fabric issue, it's just new. Give it a handful of washes before judging the hand-feel.
For the complete washing, drying, and storage routine in one place, see our Fiber Care Guide.