In Nathaniel Hawthorne's short story "The Minister's Black Veil," most everyone became terrified of Mr. Hooper the moment he donned the black veil. People trembled in his presence, and children in the streets fled from him. However, sinners whom he converted to Christianity felt drawn to him, and the dying specifically called for him to be at their death beds.
As Hawthorne phrases it, the black veil made him a very "efficient clergyman" in that it had a powerful effect "over souls that were in agony for sin," meaning over people who felt their lives had been torn apart by sin. As Hawthorne explains, sinners who saw him felt that they were "with him behind the black veil," and this perception made them feel like he was bringing light into their lives, meaning spiritual enlightenment into their lives.
Similarly, the sinners who were dying called for Mr. Hooper, refusing to leave this earth until Mr. Hooper had appeared. When he came, they felt comforted by his words of consolation but also shuddered in fear at the sight of the veil because they recognized the similarity between the veil he wore and their own souls.
As Mr. Hooper explains on his own death bed, all human beings hide their faces, their souls behind black veils because all refuse to admit to their sins. Hence, both the sinners seeking redemption and the dying sinners were able to intuitively understand the veil's meaning and to feel a special bond with Mr. Hooper for wearing the veil. The bond was formed due to the fact that, in wearing the veil, Mr. Hooper shows he understands their natures and what they are secretly going through. Yet, despite the bond, they also shrank in terror because sin, as a separation from God, and its consequences are terrifying things, just as absolute darkness is a terrifying thing.