Putting them in the microwave for few seconds appears to be the most popular and first-hand solution when it comes to making hardened candies soft again. This manner of bringing them "back to life" didn't come from any of the candy manufacturers though.
Starburst contains sugar. And there's a trick if you want your brown sugar fresh again: keep it stored with a slice of bread on top - this may work for hardened Starburst candies as well.
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Check out some great tips for storing your candy so it still tastes as fresh as the day goes by.