70 year-old Dorothy Williamson, a former Queens resident, currently lives in an Upper West Side apartment for $99/week. According to the New York Post, she used some weird legal loophole which allowed her to become a permanent resident at the Imperial Court Hotel where she was staying as a "tourist." (To the chagrin of the hotel's management.) Sure, the room is populated with plastic furniture and resembles a tomb. But Upper West Side! 79th Street! You basically have to have $1 million in the bank just to walk on the sidewalk.
This means, theoretically, a $5/month apartment exists somewhere in Bushwick.