N.Y. Suffolk County Tax Act § 70
Following each tax sale the county treasurer shall make and shall file with each town supervisor, on or before the first day of September of each year, a list of all property sold for unpaid taxes and assessments in such town remaining unredeemed. All sales of property for non-payment of taxes or assessments shall be considered arrears and be included in such list until the expiration of the redemption period as herein provided or until the property is foreclosed and notice hereof is received by the county treasurer as provided in section sixty-two thereof . The supervisor of each town shall thereupon place in a column provided therefor the word "arrears" after the description of each parcel of land as shown on the above mentioned list.
N.Y. Suffolk County Tax Act § 70