In a sublease, an entity is both a lessee and a lessor for the same underlying asset. A sublease, or sublet, occurs when a tenant assigns part or all of their lease to a new tenant.In general, most commercial leases permit subletting. A tenant who sublets an apartment to another person is the prime tenant. The person to whom the apartment is sublet is the subtenant. A sublease agreement is a legal contract signed between a tenant and a third party allowing the latter to rent out the entire property or any part of it. 1. The sublessee shall be liable for the full rent of the sublessor in the amount of. CityFHEPS is a rental assistance supplement program to help individuals and families find and keep an apartment,. The agreement between the tenant and the subtenant is known as a sublease. Tenants with a Housing Choice Voucher can't sublet.