Crisis Apparition : these are visions of persons, who at the time of their appearance are undergoing some form of crisis. For example a severe illness, an injury or even death.
The theory behind this phenomenon is that the afflicted person (the sender or agent), who is either ill or dying, sends out telepathically an image of themselves to someone who has a close relationship with them. It is thought that in general the sender or agent is unconscious or unaware of sending any message. However in the case of a death crisis, where the sender/agent actually dies, this is clearly difficult to verify.
Apparitions that are seen hours after death are put in to the category of "delayed" crisis apparitions. Some psychical researchers even go as far as to suggest that the agent transmitted the picture while still alive even if they were at the actual point of death.
In his book Apparitions the author G.N.M. Tyrell discusses a typical delayed crisis apparition. It involves a lady called Mrs. Paquet whose brother worked on a tugboat in Chicago's harbour. She awoke one morning in an unshakable depressive mood. Having gone into the pantry for some tea she turned around to see her brother Edmund standing a few feet away.
'The apparition stood with back toward me, or partially so, and was in the act of falling forward - away from me - seemingly impelled by two loops or a loop of rope drawing against his legs. the vision lasted but a moment, disappearing over a low railing or bulwark, but was very distinct. I dropped the tea, clasped my hands to my face, and exclaimed. "my god! Ed is drowned."'
Soon after this Mrs. Paquet received the news that her brother had fallen overboard nad drowned, exactly as she had seen it happen, but about six hours before her vision.
Source: Mysteries of the Afterlife, Frank Smyth & Roy Stemman, Aldus Books London 1975
The UK Paranormal Group Ghost Haunted discuss several examples of Crisis Ghosts.