I am not licensed in NY but let me just ask this/mention this.
Is the home listed with a realtor now? Wouldnt they have asked the seller what they owe, show them a estimated closing cost sheet and the seller go "hmm i dont have enough to settle the mortgage?"
Last minute things like this bother me. It should not happen. Extending settlement due to time to get some repairs I can see but this is something that should have been addressed from the beginning when the offer was made.