MacOS – My Macbook’s headphone jack stopped working, how to fix it

I've had similar issues and restarting coreaudio work for me. Run this in a terminal (you might be prompted for your password).

sudo pkill coreaudiod

If your curious sudo is something used to run commands as administrator (SU-DO as in super user do) and pkill sends signals to processes based on name, in this case coreaudiod, which is the name of the coreaudio daemon process. When it gets a terminate signal sent by pkill it will terminate and then macOS will restart it again.

Depending on the breakage, you may not be able to control the software if the "jack detection" sensor is intermittent. It will over rule whatever software setting you have made and send output to the headphone jack each time it senses an insertion.

Often taking this to Apple at a genius bar is no cost if they can dislodge the broken piece with experience (and same for reputable repair shops). Also, you might only pay labor if the jack isn't broken. Usually there is more damage since why would a protected piece break off inside a perfectly functioning receptacle, but it's possible you broke the jack mostly or entirely before inserting it.

Give a shot at setting the sound in the System Preferences, but most of the times this happens, you'll need to get a repair if you can't use software to switch the output once and have it stick.