I tried to kill Eileen after talking to her and I lost (good luck trying to parry her). Went back for my echoes and she's gone. But I dropped down to the rats, was killed by them and then I heard her voice line "Still having dreams?" Etc. So she is still somewhere in the area maybe? But not there to fight anymore.
I read there was a bug last time where she clipped through the environment but remained alive but impossible to kill. She doesn't do that anymore but she seemingly just effs off after you die and you don't get another shot at her unless you have a save close to this point you can reload. Is she still bugged?