My headphone jack is stuck in my ipad

Is the physical jack stuck or is it just showing the headphone icon when they are not inserted?

If so, try inserting and removing the headphones several times very quickly, that should release the retention clip.

I recently was listening to music And then One of my earphones was not working, wiggling the pug it soon came back. I kept wiggling it to be able to listen to both earphones but then the wire and plastic hold snapped off, leaving the whole of the metal jack in, with just about 1mm or even 0.5mm left above the actual rim of my phone. The only way I could get it out on my own without spending money or waiting 4months for something, I simply got a small tool from my draw - it was a small metal point of a plastic handle - and dragged it out with it. If you use this method be cautious not to scratch your device!