Claire's not killing anyone. She's trying to warn them. You see, sometimes spirits, they don't want vengeance, they want justice. Which is why she led us here in the first place. She wants us to know who her killer is... Detective, how much do you know about your partner?
A death omen is an apparition of a deceased person or object. Usually, a death omen is an indicator that the person who is visited by it is going to die. The apparition can manifest in several places at once (bilocation), and to different people. Sometimes a death omen will try to communicate with the person they are appearing to, in order to warn them against impending danger.BoM
Killed by a crooked detective, Pete Sheridan, The ghost of Claire Becker appeared to people he was about to murder. She tried to communicate, but could only generate the letters "DANASHULPS" through printers and computers. This was revealed to be an anagram of Ashland Sup(plies), where she was killed.
When Diana Ballard kills Sheridan, Claire is finally put to rest.
The ghost ship Espírito Santo appears to people who have murdered a member of their family, before they are killed by the vengeful spirit of the Sailor’s Ghost, the brother of the captain, who had his brother hung for treason in a kangaroo court. The ship also appeared to Bela Talbot, who does not elaborate on the reason why to the Winchesters.
After Sam and Dean summon the spirit of the Captain and allowing for his brother to confront him, the two spirits charge and merge with each other. Exploding into water upon impact. Afterwards the ship is not seen again.
In the present day, angry that other, often fake, psychics are successful while he isn't, Jimmy Tomorrow binds the ghost of Margaret Fox to kill them. Her sister Kate tries to warn the victims of their impending death, but is confused as the spirit committing the murders, and laid to rest by the Winchesters.
Dexter O'Connell was the groundskeeper of the Van Ness House in Bodega Bay, California. He was convicted of murdering the wife of his employer, Whitman Van Ness, as well as a group of women when the house became a bordello. However, Whitman Van Ness was the real killer, who shot and killed Dexter.
Dexter's spirit has been trying to warn visitors to the Van Ness house to leave before Whitman's spirit can kill them. Whitman manages to kill them anyway and he eventually drains Dexter's spirit to prevent him from scaring any more visitors away.
The ghost of a murdered young boy, Lucas Kellinger, would act as death omen to try and warn the impending victims of the ghost of Hugo Moriarty. Sam and Dean initially assumed Lucas to be a myling -- a type of child vengeful spirit in Scandinavian folklore -- though Mary believed otherwise, and was eventually proven right after learning the truth from Lucas' mother. Lucas would help Sam and Dean find the remains of Hugo Moriarty, putting a stop to him and allowing his victims to finally be put to rest.