If the 3rd baseman blocks the base without having the ball in his possession, it's obstruction, and the runner could be awarded home by the umpire, but at the very least, the runner will be safe at 3B.
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At third base : if the fielder is right handed he/she should stand with the right foot on the top left corner of the base, and the left foot and left hand outstretched toward the pitcher for a pick off move. When the pitch is thrown he/she should move off the base and into his position of fielding in case the ball is hit to him. As a left handed player it is harder to play third base. You would stand with your left foot on the top left corner of the base with your right arm and leg outstretched to the pitcher. It is harder for a lefty to play third base because you would have to tag facing the opposite direction.
He tags out a runner going to third, and can throw pretty much anywhere. He usually throws home if a runner is coming in to score. He tries to catch a lot of pop up fouls.
No, the only player allowed to be in foul territory when the pitch is thrown is the catcher according to MLB rules