The short answer
Yes. New York considers offers from people and businesses that are insolvent or discharged in bankruptcy, and from people for whom paying in full would cause undue economic hardship. Undue economic hardship generally means you can't pay basic living costs. New York uses the IRS Collection Financial Standards to judge them.
New York may require you to pay any trust taxes, like unpaid sales or withholding tax, in full first. It does not accept all offers.