Comment # 31 on bug 928394 from Takashi Iwai

OK, now it's confirmed that the jack detection really doesn't work.

Reverting back is no solution.  The root cause is that your BIOS declares that
the headphone jack is detectable although apparently it's not.

Instead, a possible workaround is to override the BIOS setup in the driver
level as if there is no jack detection possibility.  Try the following:

1. Create a file containing the lines below in /lib/firmware/alsa/nojack via an
editor (do it as root):

[codec]
0x10ec0888 0x104382fe 0
[hint]
jack_detect = no

2. Add a module option to snd-hda-intel driver; e.g. create a file
/etc/modprobe.d/50-jack.conf containing the following line (again do it as
root):

options snd-hda-intel patch=alsa/nojack

3. Reload sound modules or reboot.

With this setup, the jack detection on your system is suppressed, and PA won't
care about the jack detection.  You'd need to choose the output manually in the
mixer setup (PA lets you choose different output routes), but it's no longer
dependent on the jack status.

In the worst case, you might need to run once like
  amixer -c0 set Headphone unmute 100%