1. A journalist writes a human interest story about a member of a class of wronged people. Alternately, a lawyer finds a named plaintiff to represent a class in a class action lawsuit.
2. Legislative committees invite non-expert “witnesses” to tell personal narratives (I get the impression that Congressional committees do this more than House of Commons/Legislative Assembly committees but here’s an example).
3. Bills get written and passed that are either explicitly eponymous or coined so by journalists (eg: Grant’s Law).

You could say that politicians and journalists are into narratives because those professions are all about image. But policy analysts don’t use narratives, which I think is neglecting a powerful tool. The first significant move in this direction that I know about is the column “Narrative Matters” in the health policy journal Health Affairs. It makes sense that narratives would first be used in “tissue” policy, but I believe that sooner or later there’ll be policy narratives about small businesses, logging licenses and tax law.