Runner on base, batter hits a foul ball which is not caught. catcher throws ball back to pitcher, pitcher misses throw ball goes to outfield. can runners advance?
No. Runners can only advance on a "live ball", and as soon as a foul ball hits the ground or goes out of play, it's "dead" until that ball or a replacement is delivered back to the pitcher. The fact that the defense attempted to do so and failed changes nothing; at least until the pitcher has control of the ball it cannot become live.