May represent that something's time has come to an end - an emotional issue, a bad relationship/situatio, an era etc.
A fear of death may be the reason for this symbol - thinking about your own mortality pehraps?
Do you feel like someone is being taken away from you/ripped away - and they can't give you their time or energy or love etc?
Do you feel like you are being asked to give something of yourself that you are simply not prepared to give away?

See also 'Death/Dying'

May represent anxiety or worries about what you are saying or not saying - ex. Are you saying to much? Are you not speaking your mind enough?  Are you letting yourself ramble on an on...
Can also represent something that is hard to digest or  process, such as feelings or a problem
Chewing gum is a time waster/distractor - do you need a distraction?
Sometimes we use chewing gum to cover up bad breath - are you trying to cover something up?
Also known as chewing gum or bubble gum - note the difference and what you felt the gum was in your dream - the wording you use, could be a clue as to the actual meaning itself