Typically, when baked goods turn stale, they get hard. Yet that's not the case with crackers. When crackers turn stale, they actually become soft. This unusual reaction is due to the salt content of crackers.
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Salt is hygroscopic, which means it absorbs moisture from the atmosphere. Sugar is another common hygroscopic ingredient.
If salted crackers are left exposed to air, the salt will absorb moisture. This causes the crackers to turn soft rather than hard.
The same hygroscopic principle that turns crackers soft is also the reason why salt shakers will often clump up and become clogged when used in humid conditions.
To prevent crackers from going stale and turning soft, store them in airtight containers or bags. Any exposure to air will allow for moisture absorption.
Slightly stale crackers -- those displaying softness and not mold -- can be salvaged with some crisping in a conventional oven or with short periods in the microwave. The heat dries out the excess moisture.