iFixit sells a tool which can remove broken headphone jacks. It's called the GripStick, and you can find it here: [product|IF145-333]
This is designed for professional repair techs who have become familiar with the process over time, so it can be tricky to use at first. Occasionally, the GripStick needs to be pinched slightly near the tip in order to fit, but they do require a bit of skill and finesse to use them successfully.
''Please note that the GripStick does not have any warranty whatsoever, so there's no guarantee it'll remove the broken bit in your computer, and no returns are accepted.''