A while ago I had very unfortunate problem. I found out that the tip of my headphone connector (jack 3.5mm) had broken and stayed within laptop "female" connector.
Since there is a small pin that fixates jack within female connector, I couldn't get it out just by shaking my laptop.
You can see rough sketch of the broken connector pin in the picture.
So how to get it out? I first disassembled my laptop trying to get to the connector from within. Unfortunately that connector was fully enclosed so I was not able to get to the broken pin.
Since usage of headphones/external speakers is crucial for me, I started to think of other ways to do this.
Than I had an idea which actually worked.
What to do? Follow the steps.
Step 1: Solder the Tip of a Wire
You have to take about 6 cm of a wire, take of the isolation and solder its tip so it would be covered in tin. Wire diameter shouldn't be bigger then 3mm.
Step 2: Solder Wire to the Broken Tip
Take your pliers and soldering iron. In one hand take your pliers and grab a hold (with the pliers) of the wire. Than put it in the "female" connector so that it would touch the broken tip of the jack connector. Then take your soldering iron in other hand and put it against wire between "female" connector and pliers. Wait for a while. Holding your soldering iron against wire will eventually heat up the wire to the temperature when tin will melt. As it melts, it will solder the wire together with the broken tip of jack connector.
In the picture I have used jack connector socket to show how to do it. I pulled that tip from my laptops socket before this guide.
Step 3: Pull Out the Broken Tip
After a while try to take off the soldering iron and wait for few seconds. Tin will harden and you will be able to pull out the broken tip with your wire.