Disclosure: I saw this information on two different sites, MacRumors Forums and Reddit. I'm posting this here so that you don't have to spend the time looking for those pages.
If you are running El Capitan and your Ethernet port suddenly disappears or stops working, it may be because of this update that was pushed out on February 26, 2016:
031-51913 | Incompatible Kernel Extension Configuration Data 3.28.1
Apparently it disables the stock AppleBCM5701Ethernet driver, and prevents Thunderbolt to Ethernet adapters from working too.
You can verify if you have this update installed by going to About This Mac > System Report > Software > Installations. Sort by Install Date and check to see if you have the update above listed.
This issue affected my personal Mac Mini at home within the last 24 hours, and was frustrating me because normal network troubleshooting procedures did not produce any results. Both posts on MacRumors and Reddit had multiple suggestions on how to fix this, and I tried most of them. What worked for me was booting into my Recovery partition, disabling SIP, rebooting, installing a PKG file from Apple's software content delivery network, rebooting back into my Recovery partition, re-enabling SIP, and rebooting again.
Link to that PKG file that resolves the issue: http://swcdn.apple.com/content/downloads/47/55/031-52551/djk479pucjbs7r2ln9u3n0573nt31ifb45/AppleKextExcludeList_10_11.pkg
Many thanks to those who reported this on MacRumors and on Reddit!!! This is also my first post on JAMFNation, so I apologize in advance if I don't tag this appropriately.
MacRumors Forum Link: http://forums.macrumors.com/threads/software-update-031-51913-will-break-your-ethernet-driver.1958521/
Reddit Link: https://www.reddit.com/r/apple/comments/47tfos/warning_software_update_03151913_breaks_ethernet