Only if the lease allows it. The Residential Lease form (TXR 2001) and Residential Lease for a Multi-Family Property Unit form (TXR 2011) state that a tenant cannot sublet without the landlord’s prior written consent. A landlord can evict an unauthorized subtenant and sue the tenant and unauthorized subtenant for any property damages.
Both leases state that any subtenant must be acceptable as a tenant and sign a new lease with terms acceptable to the landlord, a sublease with terms approved by the landlord, or an assignment of the current lease in a form approved by the landlord.
The original tenant is still responsible for the lease unless otherwise stated in the sublease or assignment by the landlord. The Lease Amendment Concerning Tenant Change form (TXR 2211) includes sections to evidence a subtenant or assignee, whether the prior tenant will be released from liability, and whether and how the rent can be divided among tenants and subtenants.