There are three states for civs: Healthy, "struggling" and dead. You can embark as a healthy civ and then end up with a struggling one during game play if invaders capture your mountainhome, but there's no way to reach the dead state.
Due to accounting bugs in DF, civs that logically are long dead usually aren't according to DF, and as long as DF doesn't consider it to be dead you'll get caravans (which can go AWOL for long stretches of time regardless of civ health), unlimited migrant waves (that, again, can go missing for various reasons), and a monarch (usually very quickly, if the civ is struggling).
A truly dead civ, on the other hand, gets at most the two first waves (they can get lost due to pop caps and necro invasions), never any caravans, and never any monarch.
In addition to that, civs that DF actually consider dead are not made available for embark unless there are no civs that aren't officially dead, which is rare.
vjek's post was made several years ago, and worked with the DF version current at that time, but even a slight change to DF tends to result in the world gen/history to differ to a lesser or greater degree, killing the rare conditions that provide truly dead civs.
There are two essentially approaches to get dead civs:
1. Change the raws to spawn only one dwarven civ, and then generate worlds until you get a dead civ. This can be done with vanilla DF, and you can speed up the process by generating worlds with very short histories, embark, and check the civ-civ screen. If the screen is empty (no entries at all), the civ is dead. Save the game and start it in Legends Mode, export the world gen parameters, past those in <DF>\data\init\world_gen.txt, and change the length of the history only to generate the same world with a history if the length you actually want.
2. Generate worlds with many dwarven civs and make dead ones available for embark using the DFHack script permit_dead (
http://www.bay12forums.com/smf/index.php?topic=165084.msg7526484#msg7526484). If any civs are considered to be dead by DF, the script should make those available for selection on embark. Again, you'll probably have to generate many worlds to get a dead civ, so the short history trick above can be applied here as well.
It can be noted that I believe civs can die during world gen, but the quickest way to find them is to look for the dwarven site getting destroyed very early, rather than wait for a long time only to find that the civ usually wasn't dead according to DF.
You can increase your chances of getting dead civs by using the slab_civ script found at the link above. It basically corrects one accounting error DF does, which can lead to civs being declared dead by DF. This approach can be combined with either of the two ones above, but obviously requires the usage of DFHack.