The Last Match Loses

Two piles of matchsticks. Each turn you take as many as you like from one pile, and whoever takes the last match loses. Match the positions that are already lost for the player about to move.

Each pile is a run of 1s and the two piles are separated by a hash. An empty pile is an empty run, so "1#" is one match and none, and "#" is no matches at all. With the ordinary rule — last match wins — two-pile Nim is solved in a line: you are lost exactly when the piles are equal, because whatever you take, your opponent takes the same from the other side. The misère rule keeps that answer nearly everywhere and breaks it right at the bottom of the board, where copying stops being safe. Find the exceptions. There are not many, and they are not where you expect.