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
The ghost of Isaiah Merchant attempts to stop the ghost of his murderous daughter, Melanie Merchant, by possessing and changing paintings as warnings.
2.07 The Usual Suspects
The ghost of Claire Becker is a death omen. Killed by a crooked detective, Pete Sheridan, she appears to people he is about to murder. She tries to communicate and generates the letters "DANASHULPS" through printers and computers. This is an anagram of Ashland Sup(plies), where she was killed.
When Diana Ballard kills Sheridan, Claire is put to rest.
3.06 Red Sky At Morning
At the docks, Sam explains that ghost ships such as the Flying Dutchman, the SS Violet, and the Griffon are often considered death omens.
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 Captain's brother. The ship also appears to Bela, who does not elaborate on the reason.
After the brothers summon the spirit of the Captain and the two spirits merge, the ship is not seen again.
7.07 The Mentalists
In the 19th Century, Margaret Fox was a psychic who had a double act with her sister Kate Fox. Although Margaret had psychic talents, it was the charismatic Kate who got the attention.
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.
7.19 Of Grave Importance
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.
Annie Hawkins convinces Victoria Dodd to warn Sam and Dean about Whitman Van Ness, before she is dispatched. Sam and Dean salt and burn Whitman's remains, dispatching his spirit.