Yes, to trigger the Meat Pit you need to be below 11 Defiance, go in the sewers on the eastern part of Rathpike, in the sewers there will be a couple of thugs around a narrow hallway, if you walk in front of them one of them will accuse Claire of hurting him and that she needs to sign a bill owing him 1000 silvers, if you're below 11 defiance you will be given a choice, choose to refuse the bill and to spit on his face, the two of them will beat claire up and sell her to the Meat Pit.
To trigger the Valos Slave events you need to have slightly high intrigue (don't quite remember the number but I think it is around 5 or 6), start the quest to look for books for the expelled scholar, he lives in a rundown house in Outer Valos, after retrieving the first book the second one he requests will belong to the plutocrat family that lives in Outer Valos, knock on their door and Claire will inquire about the book, the guard will try to sell it to you for 300 silvers, if you have high enough intrigue you can threaten him by accusing him of stealing his master's books, this will make him let you inside where you will meet the master of the house, he will then drug you and throw you in his dungeon as a slave.
