In a nonpayment proceeding, if you agree to pay the back rent, the landlord's lawyer will usually require the written agreement (or "stipulation") to include a judgment against you for the sum, with possession of the apartment if you don't pay. This means that if you don't pay on time, the marshal can evict you, and after being evicted you will still owe the money.
If you agree to this, be sure the stipulation specifies that the judgment will be removed or "vacated " once you pay, so your credit rating can be rehabilitated as much as possible. Then if the landlord doesn't file papers to rescind the judgment after you pay, you can go back and ask Housing Court to vacate it.
If the landlord doesn't vacate the judgment, this also gives you the right to ask for a court order commanding the landlord to pay you penalties for failing to perform in this way as agreed in the stipulation. Currently when there is an agreement to do so, the penalty for not vacating a judgment is $100. The legislature is trying to raise that to $1,000.
Then when you get the appropriate paperwork with a Housing Court Judge's signature, you should be able to deduct $100 off your next rental payment. Send a copy of it and a letter explaining what you're doing when you pay your rent next.
Be careful - it may be to your advantage to review the facts of your case with a Tenants' lawyer to be sure you're proceeding properly.
Attention New York City Tenants: Get more more information on Landlord Tenant matters at the McAdams Law main site here.