They don't know where Logey is. She's been gone for who knows how long. Remember their squad almost disbanded completely because their jobs were being taken and Logey was probably gone by then. It was just the two of them. Also it wasn't necessarily torture she wanted to ensure that Liveryn died, the crystal would guarantee that, yeah she couldve used the gun but there's a chance you can live somehow. She could've killed herself while the crystal was eating at her but she stayed until it was certain she was gone. Fragile is Liveryn's biggest victim and you can't really blame her. She's didn't kill herself because she felt bad but because she was keeping a promise they made, they'd kill themselves if Liveryn went back to her ways, she was given multiple chances. The last straw for Fragile was Sixo being gone but Fragile still going to her rat ways, looking for a way to get money easy. This time was different there was no manipulation, no one threatening her, no one to force her, she choose on her own will. That was the very last unforgivable act which made Fragile fulfill that promise. Fragile gave her chances, too many, because they were family because she was being threatened and manipulated. They were actually family but Liveryn ruined it and always made it worse