Completely dead dwarven civs will still send liasons, merchants, and migrants in the current version, unfortunately. At least, unfortunately once you know what's going on. It is noob-friendly, so you don't gen your first world, not realize that all the dwarves are dead, and wonder why the caravans/liasons/etc. aren't working at all.
Even if world gen reaches the "age of death", where all civilizations are dead (no dwarves, humans, elves, goblins, or kobolds left alive...not sure if animal people count or not), you can still embark in dwarf mode...you'll get migrants, the home civ. caravan, and the liaison, but I think you won't get any goblin invasions, human/elven caravans, or a king. At least, that's what I hear.
I'd say I haven't tested it myself, as I haven't been playing that long, but I think I've only ever played as a dead civ...it felt pretty alive, except for no king to come make you the mountainhome, the blank entry for important civ figures, and the fact that, when you lose, legends mode ends the entry on your fort with a note that your civilization was wiped out. When I reclaimed the site, it ended up being as a different dead dwarven civilization.
You won't get migrants if you've lost a lot of dwarves (especially if some were nobles) and you haven't produced enough wealth to entice them to come anyway; embarking to a biome that's considered dangerous might also prevent them from coming, but I'm not sure what would keep the liason/caravan away, other than perhaps keeping the liaison around for several years by having a full-time military mayor, who won't meet with the liaison.