One ploy unscrupulous landlords have used is suing for rent after the tenant moved out, claiming the apartment was never surrendered. Your first defense to this is carefully documenting the end of your tenancy and return of the premises to the landlord. If you suspect the landlord may attempt something like this, you can also have your lawyer follow up with additional correspondence to confirm your departure and surrender of the unit. This shows your landlord you are represented and can defend your rights, so he or she should think twice before starting a fight. The landlord shouldn't get away with collecting double rent if the unit has been leased to someone else. For this reason it's also a good idea to stay in touch with neighbors to learn if and when the apartment is re-rented.
Attention New York City Tenants: Get more information on Landlord Tenant matters at the McAdams Law main site here.