You can only play a civ that's actually dead if every dwarven civ is dead. If there's a single dwarven civ that's struggling/dying/<whatever term you want to use>... left all the dead ones are culled from the embark civ selection list. Struggling civs are selectable along with fully healthy ones, though.
It's quite difficult to actually get a dead civ, as they have a tenacious tendency to cling to existence despite the last dwarf or other civ member dying hundreds of years ago, and a fair number of forumites claim the traits of dead civs are incorrectly described as they play "dead" civs that are actually "just" struggling and haven't drawn a breath for a thousand years (and should be dead as a door nail according to any normal criteria). I've been trying to generate dead civs to play and actually succeed, but it takes a lot of failed attempts to get one.
The only way I've found to know if a civ is actually dead when all signs I know of indicates it is is to embark and check the civ screen. If it's completely empty the civ is dead, otherwise you'll find a dwarven civ entry that expands. This expansion may still say the civ has no important leaders, but you'll get a monarch and all the rest anyway. A dead civ's mother civ appears on the civ screen at the arrival of the first caravan, together with that caravan's civ.
The basic way to increase the chance of a dead civ is to modify the dwarven entry in entity_defaults.txt to set the max number of civs to 1, to ensure a single dead civ means all civs are dead. vjek's done some further experimentation recently, but I failed to find the post when I looked for it.
Legends mode tells of a struggling civ (as displayed by Legends Viewer):
- The civ has any sites left (including "slowly repopulating" ones)
- A monarch is appointed after the fall of the last site.
- The list of wars shows ongoing wars.
Even in the absence of these indications, at least 9 out of 10 candidates turn out to just take a nap. Absence of any dwarves at all in the world is a good start, but, again, is certainly not sufficient, and, I believe, not necessary (you can certainly have dwarven necros left, and I think members of other civs might be possible, although I haven't found such a case).
The above assumes you actually want a dead civ, and not just a struggling one, as well as knowing the differences between the two cases.