
It passes straight through as far as I know. It doesn't do you any good but I don't think it does you any harm either.
My dog also does exactly the same by picking off dried on chewing gum from pavements. I rarely take her street walking where chewing gum is likely to be so it doesn't happen often. However, my children like chewing gum occasionally and have learnt to put the packets where the dog can't get to it. A couple of times I've seen her making very exaggerated chewing motions and on closer investigation found her chewing a whole packet, thick silvery paper wrappings and all :rolleyes: Makes their breath smell sweet though doesn't it :P :D