A tenant can sublease the leased property or assign or encumber their rights under the lease. This is the case unless the lease has specific language which prohibits this.
Assignment vs. Sublease
An assignment is when the lessee assigns their rights under the lease to fulfill their lease. This includes paying the rent to the lessor. After an assignment, both the original lessee and the new lessee still promise to pay the lessor. The lessor is the 3rd party beneficiary to the assignment.
A sublease is the transfer of a lessee's right of occupancy. The sublessee does not promise to pay rent to the lessor. The sublessee must pay the original lessee. The original lessee is still bound to pay the lessor.
Whether a lessee assigns or subleases a property, they are still liable to the lessor to pay rent. This can only change by agreement with the lessor to release a lessee from liability to pay rent.