I think I have experienced it. I felt like one of my supervisors was a second father to me; I felt like my neighbors next door were grandparents to me.

In psychology, transference is this: (oops, wrong link--just fixed it)
Transference | Psychology Today

Transference can be a good feeling (the examples I cite above); it can also be messy. If you read some of the posts in the psychoanalysis forum, it shows how sometimes people develop romantic feelings for their therapist--we know these feelings are inappropriate but when a person is not used to getting loving attention--sometimes our emotions overreact. We all need love and attention.