Yes, but of course Sauron knew very well at that time that the Ring is with Frodo and there was no reason to search the Fields anymore. But he may not have called off all of his servants, exactly for the reason mentioned above - so that no one passes through if they choose to. Also, we know that Saruman was searching that area extensively before as well. So maybe some of his "friendly fellows" remained there also.
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"Should the story say 'he ate bread,' the dramatic producer can only show 'a piece of bread' according to his taste or fancy, but the hearer of the story will think of bread in general and picture it in some form of his own." -On Fairy-Stories
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