In NYC, BOE doesn't even appear to have a replacement ballot option. You can request another ballot apparently (which, uh, would be mailed to you and at the whims and delays of USPS) or you can go vote in-person and hope they know how to properly do (and store) an "affidavit" ballot. https://elections.ny.gov/request-ballot
If you can't physically get to the polls and it's too close to election day - tough luck, I guess?