What is the statute of limitations on past due rent in NY?

The statute of limitations for breach of contract in NY is 6 years.  However, if your former landlord sued you and obtained a default judgment for the rent (assuming you were not aware of the small claims matter), then the statute of limitations to collect on that judgment is 20 years.  It is possible your former landlord sold the judgement and the letter you received was on behalf of a collections agency. https://statelaws.findlaw.com/new-york-law/new-york-civil-statute-of-limitations-laws.html