They can but it would just be dumb.
Actually, the first baseman cannot stand in foul territory. The only defensive player allowed to lineup not in fair territory is the catcher, who must take his position behind home plate in the "catcher's box", which is technically in four territory.
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I'm going to answer the question, "Can a bAlk be called if either the first or the third baseman are in foul territory?" as well as "Can a balk be called if the runner on first or on third base are in foul territory?"
A balk is called whenever the pitcher makes an illegal throw or pitch. Basically, if a pitcher moves his front foot toward a base (including home plate), it must be that base that the pitcher throws the ball towards. The location of the either the runner or the fielder is completely irrelevant to whether or not the pitcher committed a balk.
From the best of my knowledge the player can not be positioned in foul territory but is allowed to enter foul territory to retrieve or catch a foul ball.