I can think of two sources for evidence for such a case.
1. The most accessible to us is ghost phenomena. There is considerable anecdotal evidence that ghosts have been seen by some but not all people, as well as heard, smelt and felt.
It also appears that IR photography can detect ghosts even when they are not seen in the visible. My girlfriend, a professional photographer, has a colleague that takes IR pictures everywhere he goes and more often than not finds orbs in the developed film.
I have no physics hypothesis on how this can occur. Peter Sikivie(Sp?) of Florida State has a theory that axions stimulate photons in a magnetic field. That has been used to try to detect axions but so far without success.
2. Also, in Hindu scripture and in some popular yogi books it is said that Gurus, etc., can appear to their disciples. I most recently read of this in "Autobiography of a Yogi" which has many experiences that are suggestive of interesting physics.
One of the most interesting is when the yogi, still a student, was given the ability to see through walls by his Guru. What he saw in that state was that everything was shimmering, both the cow behind the wall and the wall.
That suggested to me that he was able to see fields or quantum functions in that state because the probablistic nature of the fields made them shimmer.
I of course hypothesize that he was able to see the axion condensate image of physical things on an axion condensate channel. Perhaps we all will after death.
All the best,