A judgment is when the court decides you owe money or you must move out. If you consent or agree to a judgment in your stipulation and don’t pay on time, the judgment allows your eviction to go forward. Judgments can be in stipulations, or can be issued after trial if you have one. (Most cases in Housing Court are settled and have stipulations. Very few end in trials.)
There are two types of judgments that come out of a Housing Court case. A final judgment in a nonpayment case generally provides for both a money judgment and a possessory judgment. The money judgment is usually the amount of back rent owed. The possessory judgment awards the apartment to the landlord.
In a nonpayment case, when the money owed is paid, the money judgment is satisfied and the possessory judgment goes away. However, if you do not pay on time, the possessory judgment, combined with the warrant, allow the landlord to get a marshal to evict you. Even if you are evicted, the money judgment stays in place until it is paid.