Why is the 4th ghost the only ghost that isn't violent?

I believe that it had to do with her connection to them, since she was their mother/wife. None of the characters shared any similar connection to the ghosts.

Also, Jean is the only one that died in a non-violent, non-demeaning manner. Yes, she died in a fire, but she was saving her family, not trying to murder them.

13 ghosts are required to make a dark Zodiac. As in the zodiac there are 12 zodiac signs, which says that every member who belongs to that sign has some specific traits. Similarly, we can assume that the 13 ghosts required for making Dark zodiac should also have different traits. For example, the 13th ghost is Arthur, whose soul is required, but he is also nonviolent.

Most of the ghost are violent, but they have their own traits that make them different from each other. The The Withered Lover is a spirit made of sacrifice, so she doesn't have any vengeance towards anybody, which made her nonviolent.

As is stated on Wikipedia, ghost #4 is called The Withered Lover ...

It is written as such:

The Withered Lover is Jean Kriticos, Arthur's wife. She was burned severely while saving her family from a devastating house fire, and died of her wounds in the hospital. Her ghost initially appears in a hospital gown, hooked up to an IV pole and showing severe burns on her face. However, after the destruction of the machine, her ghost is wearing her normal clothes and her burns have vanished. Unlike the other ghosts, she is not a vengeful spirit and tries to help her family.