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Runner on 1st, ball is hit between 3B & SS and fielded by SS who tags 2nd for a force out and throws to 1st attempting double play. 1B is not positioned on inside of bag and ball bounces off batter/runner as they cross the bag and over the fence. Batter/runner is awarded 2nd due to ball being out of play, same as if it had rolled in a dugout. Should there be an error assigned to anyone on this play?

Yes, someone needs to be charged to account for the runner advancing. Generally, if a throw hits the runner, the thrower is charged.

Yes......double play can't be assumed......so it would be a fielders choice (recording the out at 2nd) and the batter reaching second on the throwing error on the shortstop.