N.Y. Elec. Law § 10-116
The state board of elections and the county boards of elections shall determine, three days before the first day for distribution of military ballots, the names of all candidates duly nominated for public office and the amendments, referenda, propositions and questions to be voted for on such ballots. If at a later date the nomination of any candidate named on a military ballot is found invalid, the ballot shall still be valid, but no vote cast for any such candidate on such ballot shall be counted at the election. The failure of the county board of elections to include the name of any candidate or any amendment, referendum, proposition or question on the military ballot shall in no way affect the validity of the election with respect to the office for which the nomination was made or the validity of the military ballot as to any other matter.
N.Y. Elec.Law § 10-116