I can't find Karliah at the Ragged Flagon

I did this on the PC last night and I couldn't enter the Ragged Flagon from the back entrance as the key seems to have changes.

I had to go through the Rat Way like the first time.

And then she was waiting right after you enter the Ragged Flagon.

If she is not there, maybe try to wait for a while. She might be slower at getting there than you (if you used fast travel right after she told you to meet up there).

I found Karliah at the Snow Veil Sanctum, in the room where I got poisoned, stuck at the door at the top of the stairs. Just open the door exit and this should solve the problem.

Wait a couple of in-game days for her in The Ragged Flagon. Wait in 24-hour intervals, and see if she shows up. Karliah sometimes takes a long time to travel.

If that doesn't work and you're playing on the PC, an alternative workaround is to use console commands to teleport Karliah to your location. Open the console by pressing ~.

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 in the UESP wiki.