Is there a stone that weeps?

I just finished watching the Pillars of the Earth miniseries and in episode 7 there is a "stone that weeps at night." I am guessing that this is a white mineral that absorbs moisture when it is heated by the sunlight, then at night when it cools it releases the moisture and appears to weep. I am just curious if this mineral actually exists or if it is something the writers made up for the story. I tried Google and found nothing. Does anyone know?