Read the form to see if there are any deadlines ... probably not since the return is just in limbo until you respond. Worse that can happen is that you would have to refile the return later. If you can get someone to save the W-2 forms as a PDF then you can send it to them as an attachment.... just set up an online account it is really easy.
https://www.tax.ny.gov/pit/letters/dtf-973.56-o.pdf
