The Black-haired Painting seems to be the portrait Mona Lisa painted by Leonardo da Vinci, as well as the other paintings in the room, apart from their hair colours. When Viola is caught, her expression changes to a grim smile with darkened eyes.
Once Viola receives the Music Sheet from the wall, the black-haired lady will come out of her painting. All doors in the room will be locked until you tear down the painting where the woman came from. If you return to this room after solving the Piano Puzzle, the dark-haired woman will be seen peeping from her distorted painting. If Viola gets caught, she will be transformed into a portrait of herself and fall to the ground.
If you run from her for too long, she will turn red and it will be impossible to outrun her. When she catches Viola and turned into a portrait she will be all bloody and have no eyes.
In Extra Mode, her role of being the 4th Floor's pursuer is replaced by the Toy Soldier, though if you interact with the painting while the Toy Soldier is chasing you, the Black-haired painting will come out and turn Viola into a portrait.