In "The Purloined Letter," Poe brings law enforcement front and center. But maybe "law enforcement" is too strong of a phrase; maybe it's more like "law-breaking enabler." After all, the story seems more interested in showing that the upper echelons of the society in which it is set are devoid of law and order. From Dupin to D— to G— to the royal lady herself, most of the characters are total crooks. By presenting a society where rulers, politicians, police, and private detectives depend on deception, "The Purloined Letter" questions the very role of law and order.
It's fitting that G— has the letter at the end of the story, because, as the story's representative of rules and order, he now has the power to restore order to the community either through revealing or continuing to conceal the letter.
Because the people in charge of maintaining order in society (rulers, police, detectives) in this story are wholly corrupt, we can assume that there is little order in the world of "The Purloined Letter."