This stone looked nearly the same, but it wasn't. It was the Omission Stone, which worked just like the original stone, but after every wish, someone who was considered "close" to the wisher (relationship-wise) would be erased from existence. Reality would change as if they never existed in the first place. Only the wisher would notice that the person was missing.
But these "omissions" weren't permanent. Once a person had been erased, someone could wish them back, but since that's another wish, another person would be erased from existence.
Jessica walked towards the spot where she usually met up with her friends before school. And as she approached Lucy Corinth (her ditzy friend), she took out the stone, completely unaware that it wasn't the same stone she inherited from her grandfather.