psychofactz:

Thats just a myth. When we say that gum is “indigestible” we don’t mean that it stays in your body. It just doesn’t break down much when you chew it in your mouth or when it passes through your digestive system. Nothing bad will happen to you if you swallow gum. It comes back out of your system just like anything else.Except that it will look pretty much the same going out as it did coming in. 
~Source!
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psychofactz:

Thats just a myth. When we say that gum is “indigestible” we don’t mean that it stays in your body. It just doesn’t break down much when you chew it in your mouth or when it passes through your digestive system. Nothing bad will happen to you if you swallow gum. It comes back out of your system just like anything else.Except that it will look pretty much the same going out as it did coming in. 

~Source!

More Facts on Psychofacts :)