Let's say you're using Ubuntu 13.04 (Raring Ringtail, released in April 2013) and it just went End-of-Life on you, because it's supported for only 6 months, and the deprecated packages are taken down after 12 months.
You'll probably figure this out the hard way. When you run sudo apt-get update, it will eventually report these errors:
Ign http://archive.ubuntu.com raring-updates/universe Sources/DiffIndex
Err http://security.ubuntu.com raring-security/main Sources
404 Not Found [IP: 91.189.91.15 80]
Err http://security.ubuntu.com raring-security/universe Sources
404 Not Found [IP: 91.189.91.15 80]
Err http://security.ubuntu.com raring-security/main amd64 Packages
404 Not Found [IP: 91.189.91.15 80]
Ign http://archive.ubuntu.com raring-updates/main amd64 Packages/DiffIndex
Err http://security.ubuntu.com raring-security/universe amd64 Packages
404 Not Found [IP: 91.189.91.15 80]
W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/raring-security/main/source/Sources 404 Not Found [IP: 91.189.91.15 80]
W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/raring-security/universe/source/Sources 404 Not Found [IP: 91.189.91.15 80]
W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/raring-security/main/binary-amd64/Packages 404 Not Found [IP: 91.189.91.15 80]
W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/raring-security/universe/binary-amd64/Packages 404 Not Found [IP: 91.189.91.15 80]
Visiting http://archive.ubuntu.com/ubuntu/dists does confirm that raring packages are indeed gone, while lucid, precise, saucy, and trusty are still there, as per their promised support schedule.
Some googling reveals that they're not deleted, but simply moved to http://old-releases.ubuntu.com/ubuntu/dists/, sort of a graveyard for insecure and unsupported packages.
To make apt-get update work, we simply need to edit /etc/apt/sources.list and update all URLs from security.ubuntu.com and archive.ubuntu.com to point to old-releases.ubuntu.com, as per the following sed command:
sudo sed -i.bak -r 's/(archive|security).ubuntu.com/old-releases.ubuntu.com/g' /etc/apt/sources.listAfter this, sudo apt-get update seems to run without a hitch. Of course if you do this, you're accepting to use an insecure system, and should do sudo apt-get install update-manager-core; do-release-upgrade as soon as possible.
SOURCES:
I would like to add this link in case you get NO_PUBKEY error:
http://askubuntu.com/questions/1877/what-is-the-easiest-way-to-resolve-apt-get-badsig-gpg-errors