A bit of an issue...

[BBN]

saw a similar discussion somewhere, and the person used a plastic straw of correct diameter (large enough to match the inside diameter of the jack). The idea was to push the straw into the jack and surround the broken off tip, then slowly pulling the straw out with the unit/jack tilted downward so that gravity helps it to come out with the straw.

Interesting approach. I might try a pen cap (with the end cut off) as it's a bit more rigid and would release the tension on the springs.
But overall, this seems like a simple and logical approach.
Put something in to release the tension....use gravity to help it fall out.