If you can't remove headphone plug from PC, why not remove PC from headphone plug.. Jokes aside, try dabbing it with an earbud soaked in some oil. Then pry it out slowly, careful not to scrape or damage the port itself.
if there is still a sizable part of the headphone sticking out of the hole you can use pliers. If its all inside or not part sticking out you either have to live with it or disassemble that part of the PC
what abcwan said use a stick, not bigger than the 3.5 mm hole use a glue and try to stick the stick with the broken jack, wait for the glue to dry then you can pull the broken jack by pulling up the stick or you can just use a pinset or plier if there's a part that you can clamp from the broken jack
If you are desperate and there is nothing left on the outside of the port to grab (how the fuck does this even happen), you can buy quick curing epoxy, dab a small wooden stick with it, and stick it to the thing inside, wait for it to cure, then pull it out. If it's even deeper, you can try diddling it out with a pin needle. If it's very deep, you can try drilling it out, but the port will get damaged.
I'll just make a note to make sure you have your computer unplugged while you are messing around. You never can be too careful with electrical equipment.
Would you believe they make a specialized tool for this? Google 'Gripstick'. It's for phones more than PCs, I suppose, but a 3.5mm jack is a 3.5mm jack. Otherwise, just google the problem in general. There are a dozen suggested methods. Some of which are: Inside of a pen. Supergluing the rest of the connector plug. Thumbtack with a bent point A toothpick with hot glue. A heated paperclip.
Worse comes to worse... - Remove the board, - find a replacement on Mouser or Digikey, - Wait for the replacement to arrive in the mail... - desolder the original 3.5mm jack - solder the new 3.5mm jack God forbid the 3.5mm jack is surface mounted though...
everyone already said what I was gonna so my answer is "throw it into the fires of Mount Doom and be done with it"
i've remove broken+stuck 3.5mm minijack tip a several times throughout the years, and it depends on how much of the broken tip was inside. if there's a lot of it, then using a very slim tweezer could work. otherwise, i would recommend @Westeller 's method 1 or 4, or a combination of both. but do not use hotglue if you've never use one. i've never tried the other listed methods (2, 3, 5), but i did tried other, more extreme methods, however 99% of the time, you won't have to. actually, with method 1, you might not even need to use a glue at all, assuming you can find the right pen. see the video below for better explanation Spoiler on some older pc motherboard, or pci/pcie sound card, it is even simpler. all you need is a needle to push out the jack from the opposite side.
Spoiler: Deleted answer. If some one still need the answer to removing broken male 3.3mm jack stuck in a female 3.3mm jack, depending on the type, you can try opening up the case and stick a metal wire to open up. As for the seal off type, best to replace the female jack all together. Those usually only cost 1yuan to 4yuan each in China, and usually shipping included. You only need to solder 2 contact points for without headphones. Pretty easy. 3 point with headphones. If some one unfortunately resin the plug, for waterproof or dust proof, (I have never seen it on pc, only on radio) it will be harder to remove. You should just try you luck with whatever method, or just sent it to some one who deal with electronics, they should know what to do. Edit: oops necro posting.