Although chewing gum is designed to be chewed and not swallowed, it generally isn't harmful if swallowed. Folklore suggests that swallowed gum sits in your stomach for seven years before it can be digested. But this isn't true. If you swallow gum, it's true that your body can't digest it. But the gum doesn't stay in your stomach. It moves relatively intact through your digestive system and is excreted in your stool.
On very rare occasions, large amounts of swallowed gum combined with constipation have blocked intestines in children. It's for this reason that frequent swallowing of chewing gum should be discouraged, especially in children.