The headphone jack is metal, while the ball is softer plastic. The following may work:

1. Find a very tiny drill bit that can slide easily inside headphone jack.
2. Wrap a piece of Scotch tape around the bit next to the tip, leaving the tip exposed.
3. Hole the bit with your fingers (not a power drill!!), and slide it into the headphone jack. The Scotch tape around the bit should protect the inside of the jack, but the exposed tip should be able to grind away at the ball.
4. Rotate the bit back and forth with your fingers, apply a little bit of pressure. The plastic ball should "erode" into smaller bits of plastic. I imagine you'll be able to tell when it's gone, or you could pull out the bit every few rotations to check on your progress.
5. When you're done, you can tip up the computer to dump out some of the plastic shavings, and clean out the rest using compressed air or a wooden toothpick.

Note to electronics experts: If this is a terrible idea because it will ruin the jack despite the Scotch tape around the bit, and I get enough comments and thumbs down, I'll remove this answer.

The headphone jack is metal, while the ball is softer plastic. The following may work:

1. Find a very tiny drill bit that can slide easily inside headphone jack.
2. Wrap a piece of Scotch tape around the bit next to the tip, leaving the tip exposed.
3. Hold the bit with your fingers (not a power drill!!), and slide it into the headphone jack. The Scotch tape around the bit should protect the inside of the jack, but the exposed tip should be able to grind away at the ball.
4. Rotate the bit back and forth with your fingers, apply a little bit of pressure. The plastic ball should "erode" into smaller bits of plastic. I imagine you'll be able to tell when it's gone, or you could pull out the bit every few rotations to check on your progress.
5. When you're done, you can tip up the computer to dump out some of the plastic shavings, and clean out the rest using compressed air or a wooden toothpick.

Note to electronics experts: If this is a terrible idea because it will ruin the jack despite the Scotch tape around the bit, and I get enough comments and thumbs down, I'll remove this answer.