N.Y. Elec. Law § 8-316
If a ballot is found to be defective or mutilated before it is delivered to the voter, its stub and the stubs of all other ballots in the set shall be detached immediately and placed in the box for stubs, by the clerks, or if there are no clerks by the inspector assigned to the duty of delivering ballots, and all the ballots of that set immediately shall be marked "cancelled", and placed in the box for spoiled and mutilated ballots. If a voter returns a ballot as defective, mutilated, defaced, or wrongly marked, he shall also return all the other ballots of the set, if any, and such clerks or inspector shall likewise remove their stubs, placing all the stubs in the box for stubs and all the ballots of the set in the box for spoiled or mutilated ballots, first marking the ballots "cancelled". In each case, the voter shall receive another ballot or set of ballots, unless not entitled thereto.
N.Y. Elec. Law § 8-316