Did you have an attorney? If so, then please ask your attorney to follow up for you.
if you gained an eviction of the tenant by the successful prosecution of a nonpayment proceeding then you should have a money judgment for the unpaid rent, that was entered along with your final judgment for possession. It is the failure of the tenant to pay the money judgment that allows for the expiration of the stay of the issuance of the warrant of eviction and for the landlord to then proceed to execute on the warrant and "evict" the tenant.
That is the main point of the nonpayment summary proceeding. If the court allowed the eviction to go ahead then the tenant did not timely pay the money judgment entered in the nonpayment proceeding. That does not mean that the money judgment evaporated because the tenant did not pay and the landlord was allowed to proceed with the eviction.
So you have to know what happened to your money claim in the nonpayment proceeding for any more information.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
As the tenant has already moved out, there is nothing you can do in housing court. You'll have to sue her in a regular-type law suit in Supreme Court, where the property is located, or where your LLC has its principal place of business. Unless you had a written lease with her and she claims that you forced her out, it sounds like it will be fairly easy to win the case. The problem will be collecting any judgment you may be awarded.
If she paid rent by check when she paid, find the name of the bank, and issue a restraining notice to judgment debtor. Remember - you can only do this after you've been awarded a judgment, for the amount set forth in it. You can also restrain neighborhood bank near where she lives. You will have the right to compel her to produce all books and records pertaining to her business, as well as her personal finances, and you can subpoena a witness with knowledge of her business dealings, if you can find one. There are other things you can legally do to collect a judgment.
For $25K, it'd be worth your while to hire an attorney. See if you can find one who'll take the case on a contingency fee basis.
I am an attorney admitted solely in NY. None of the answers I submit on this forum constitutes legal advice, even to questioners in NY, and no attorney-client relationship is hereby created.
You would have to start a separate lawsuit for the back rent. Since your company is an LLC, you would need to hire an attorney to bring the suit. It appears to be worth your while for $25,000 in damages.