Wool doesn't really wear out in a drawer. It gets eaten. The thing that ruins a stored shawl isn't the passing of time, it's a moth, or rather the moth's larvae, which spend the warm months quietly chewing holes in anything you forgot to protect. Get the storage right and a good piece will come out in autumn exactly as it went in.
Clean it first, the bit people skip
Clothes moths aren't after the wool itself. They're after what's on it: sweat, skin oils, a drop of food, perfume. A shawl that's been worn a few times and put straight away is a buffet. So before anything else, wash it or at least air it thoroughly. A clean piece is a far less interesting meal, and that single step prevents most damage. Our Guide to SHAAL covers washing if you're not sure.
Fold, don't hang
Over a winter, hanging is fine. Over six idle months, the weight of the wool slowly drags itself out of shape on a hanger, and that stretch doesn't come back. Fold it instead, loosely, and lay it flat. If you're stacking several, put the heaviest at the bottom. A dense piece like a heavyweight wool shawl is the one to watch, since its own weight does the damage fastest.
Let it breathe
Do not seal wool in a plastic bag or a vacuum sack. Plastic traps any leftover moisture, and trapped damp invites mildew and that musty smell. Worse, if there are already moth eggs in the fibres, plastic just gives them a sealed room to hatch in. Use a cotton or linen bag, or a box that isn't airtight. Wool needs a little air.
Deter the moths
Cedar and lavender both put moths off. Not a force field, but a real deterrent. Tuck a cedar block or a lavender sachet in with the folded pieces. Cedar fades after a year or so, and a light sand with fine paper brings the scent back. The old mothballs work too, but they smell like a Victorian wardrobe and you'll regret it in October.
Keep it cool, dark and checked
A cool, dry, dark spot is ideal. Moths and damp both prefer warm and forgotten. And once, around midsummer, actually open the drawer and look. Sixty seconds now beats finding a row of holes when the cold comes back.
That's the whole method. Clean, fold, breathe, deter, check. And if you're storing different fibres together, it helps to know what each one is, which our guide to the types of wool sorts out.