Mercer will inform you that Karliah is hold up inside Snow Veil Sanctum, so lead the way to the door, which Mercer will unlock, and head inside.
A possible solution is to go to the Flagon and move her via console commands: prid 00058F1A to select Karliah, followed by moveto player to move her to you. You may need to manually advance the quest as well with setstage tg07 20 .
Track down the Dunmer behind the Guild's misfortunes. Quest Giver:Mercer Frey Next Quest: Hard Answers Reward: Gallus' Encoded Journal, Word for the Disarm shout ID: TG05 Suggested Level: 62 more rows •
Karliah and Brynjolf have traveled to Irkngthand in their pursuit of Mercer Frey. They want the Dragonborn to meet them there. Inside they need to locate and eliminate Mercer and take the Skeleton Key he has stolen from Nocturnal.
Track down the Dunmer behind the Guild's misfortunes. Quest Giver:Mercer Frey Next Quest: Hard Answers Reward: Gallus' Encoded Journal, Word for the Disarm shout ID: TG05 Suggested Level: 62 more rows •
If you have already completed the related Thieves's Guild quest, the claw is easy to find (In the final room, near the alternate exit). If you haven't finished the quest, you won't be able to reach it yet — also, the cutscene will make it fall from it's resting place (pictured above) onto the floor.
After the main Guild quest she resides in Nightingale Hall. Karliah's unique outfit consists of her armor, her gloves, her boots, and her hood.
You can find it by traveling South East of Winterhold and North Northeast of Windhelm. The Main entrance is locked and requires a key to open it. The door is unlocked during the quest Speaking With Silence.
You can't marry her in the vanilla game. She can't even become a follower in the vanilla game. But I assume there are mods to change that.