Where is Karliah and why haven't I been given the follow-up quest? [duplicate]

After the quest "Hard Answers", Karliah told me to meet her at the Ragged Flagon, but it never came up in my journal or even came up as a quest.

I go to meet her at the Ragged Flagon and she isn't there. Tried going back to the Sanctum where we first met and she was there, trapped behind a door. I opened the door to free her and tried talking again but she doesn't say anything. I tried going back to the Ragged Flagon again but she still is not there.

As mentioned by agent86, you could try waiting a couple of days (in-game) for her in The Ragged Flagon.

If playing in the PC, an alternative workaround is to use console commands to teleport Karliah to your location.

Console commands to teleport Karliah to the player's current location (make sure you are in The Ragged Flagon before you input the commands):
prid 58F1A
moveto player

prid targets an entity - Karliah in this case. '58F1A' is Karliah's RefID. moveto player moves that targeted entity near the vicinity of the player.

Karliah should now be near you after doing this.

More info on console commands here: http://uesp.net/wiki/Skyrim:Console

Type

recycleactor 00058F1A

in console