Unless the lease allows it, a tenant may not sublet (rent the house or apartment to another person) without the consent of the landlord. Tex. Prop. Code 91.005 If a tenant sublets the house or apartment without the consent of the landlord, the landlord may evict the subtenant and sue both the subtenant and the original tenant for any damages caused by the subletting arrangement.

Landlords do not like subletting in general because you are getting into their business. If you are renting out their place for more money, they want to be making that extra profit and not letting you keep it. And if you are subletting because you could not stand the place or you could not afford it or got transfered or some other good excuse, you are not giving the landlord the chance to rip you off -- if you prematurely terminate the lease then they of course will get even more of your money. Then they can rent the place out again and hope they have to move early too.

If the lease does permit you to sublet your place, subletting is still complicated. Unless the subletter (the person renting from you) and the landlord sign a lease agreement with each other, you will become the landlord of the new tenant. For example, your subtenant will have to request repairs to the apartment from you. You will then have to request the repairs from your landlord. Moreover, you remain liable to your landlord for the rent. So, if your subtenant stops paying rent, you will have to pay rent to your landlord and attempt to seek reimbursement from your subtenant. You will also be liable to your landlord for any damage done by your subtenant. If you must move out of your apartment, you should attempt to get your landlord and the person moving into your apartment to agree to a lease between each other. You should have your landlord release you in writing from any further liability under your lease. This will avoid the undesirable situation where you are stuck in the middle between your landlord and your subtenant.