Employment Law Questions? Ask an Employment Lawyer.
ANSWER: New York is considered to be an "employment at will" state. This means that an employer can for the most part fire an employee for any reason or no reason at all and the employee usually will have no legal recourse even when the discharge is unfair or unreasonable. That said, the employer cannot fire you or harass you based on your race, religion, nationality, gender or sexual preferences. Further, if you have a signed contract for employment for a particular term or duration, then the contract as well as any write-up or termination policies in an employment handbook must be followed uniformly across all employees. Finally, they cannot harass or fire you because you report or threaten to report an employer's violations of the law to the government or stand up for your rights as an employee.
In your case, it appears that they are not willing to terminate you hoping that you will leave on your own so that they don't have to pay for unemployment. But, based on what you have mentioned, I don't see a viable case here. I know this is not the answer you wanted to hear, but I am assuming that you are paying for a professional and honest answer.