What can happen to you overtime if you swallow gum?

Probably no issues. The gum most likely will be passed through the gastrointestinal tract and you should be fine. If you do experience any constipation or abdominal pain then consult your md.
Likely nothing. I trust you are talking about chewing gum. Swallowing chewing gum, while not recommended, is not likely to cause any problem in an otherwise healthy person.