Q: OS X 10.11.6 update - fire wire gone

Hi Sascha, do other firewire devices work in the port? Shut down your Mac and disconnect your firewire cable from both ends and let it sit about ten minutes then reconnect and try. Also, it is important to  disconnect the AC power to your Mac, this helps to reset the FireWire port(s).

It seems like a bad firewire port. Take your Mac to any Apple Store for a free diagnosis. You might do a check with Apple Hardware Test or Diagnostics depending on the age of your Mac.

Using Apple Hardware Test - Apple Support

I's advise taking it to any Apple Store for a free evaluation they have much better propratory software that does a much deeper check than AHT.

Long shot. Try running the combo update. It installs all previous updates plus the new one, which can replace any files that may have become corrupted.

10.11.6 combo update