I recall meeting someone on Yom Kippur once who would not respond when I spoke to him. Instead he handed me a piece of paper which said that he was engaged in a taanit dibur, a 'fast' where that which one is refraining from engaging in is speaking. I would like to know where this idea comes from.
This site says there is no source for the Taanis Dibbur but that it is mentioned by the Mishnah Berurah 571 (1) MB  where the Mishnah Berurah says that he saw written in a book that when someone wants to offer a voluntary fast it's better if he accepts a Taanis Dibbur rather than holding himself back from food since he will have no bodily harm from it (he will not get weak as in a fast from eating and drinking). He points out that the Vilna Gaon in a letter wrote that a person should not afflict himself with fasting or other bodily afflictions but rein in his mouth and his appetites.