The stranger behind the mask is the Red Death itself. Of course, the entire thing is metaphorical of the disease entering the supposedly secure protection of the fortress, and the relative safety of the party. Yet, Poe describes the stranger as:
"....tall and guant, and shrouded from head to foot in the habiliments of the grave. The mask...was made...to resemble the countenance of a stiffened corpse....But the mummer had gone so far as to assume the type of the Red Death. His vesture was dabbled in blood-and his broad brow, with all the features of the face, was besprinkled with the scarlet horror."
It was after the attendants tried to get the stranger, that they found out, with horror, that this figure is basically the representation of the red death itself they:
"...gasped in unutterable horror at finding the grave cerements and corpselike mask...untenanted by any tangible form."
So, the disease entered the secluded place: Sometimes the enemy is in front of our eyes.
This is, as many of Poe's short stories are, a very symbolic piece of fiction, where you would be advised to look for how events, characters and the setting operate symbolically. It is clear from the description of the uninvited guest that he represents death and the way that no matter how hard we try, we are unable to escape, cheat or run away from death. It is key to note that when Prospero challenges this guest they are both standing in the blue room, and then the guest walks through all the seven rooms (seven indicating the seven stages of life and the seven stages of man) to the black room, symbolising the last stage of life. Note too that this guest is seized when he is standing in "the shadow of the black clock," itself a symbol of time passing and the brevity of life. This all points towards the guest as being "The Red Death" itself, or death, that Prospero and his revellers were unable to cheat.