Title of a movie, in which people are cured by touching a piece of sacred cloth, which shrinks a bit each time

Somewhat similar in content to an episode from "Mysterious Ways", in which Miranda is dying and only touching the cloth can cure her - but then the remaining bit will fade away entirely, forfeiting an opportunity to test it and perhaps to find an universal cure. I am sure I saw the same dilemma in another movie, but I can't remember where.