If a tenant no longer wishes to continue their lease, one option is to do an assignment. An assignment of a lease is a transfer of the remaining rights and obligations in a lease from one tenant to a new tenant. The old tenant is called the "assignor" and the new tenant is the "assignee."
Generally, the lease will say whether or not an assignment is permitted. If not, state law determines whether the tenant can do an assignment. For example, under Texas law, if the lease does not provide otherwise, an assignment requires the prior consent of the landlord.
Even if the lease prohibits assignments, the landlord may waive this restriction and allow the tenant to assign the lease. The landlord's waiver may be express (i.e. by the landlord's own words allowing the assignment) or implied (i.e. by the landlord's conduct, such as accepting rent from the assignee).
Note that an assignor is NOT released from contract obligations merely by assigning the lease to another. The assignor remains liable under the original lease contract unless the landlord expressly agrees to release the assignor from further liability under the lease contract.
