This is from a short story by O. Henry called "The Last Leaf."  I want to ask the meaning of the following sentence: In a little district west of Washington Square the streets have run crazy and broken themselves into small strips called "places." These "places" make strange angles and curves. One Street crosses itself a time or two. An artist once discovered a valuable possibility in this street. Suppose a collector with a bill for paints, paper and canvas should, in traversing this route, suddenly meet himself coming back, without a cent having been paid on account!

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In this passage that you quote here, the first three sentences are simply a description of a part of Manhattan (in New York City) that is called Greenwich Village.  The author is saying that the streets of this area are not straight and easy to follow.  Instead, it is like...

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In this passage that you quote here, the first three sentences are simply a description of a part of Manhattan (in New York City) that is called Greenwich Village.  The author is saying that the streets of this area are not straight and easy to follow.  Instead, it is like a maze of small streets.

As for the rest, Greenwich Village was known as a home to artists and other people (often poor) who did not like to conform to what society expected of them.  O. Henry is making up a reason as to why this happens.  He says that artists liked to live there because bill collectors could never find them to make them pay their debts.

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