The question sates that "stuff" was left behind on the day that the lease was terminated. It does not saw whether the tenant notified the landlord of this stuff, much less sought permission to leave it. It does not say when or if the tenant removed the stuff, how much stuff there was, or whether the landlord would have had to remove it before the premises could be cleaned and rented to a new tenant.
The exact provisions of the lease are going to matter a great deal here.
Chapters 91 and 92 of the Texas Property Code cover statewide laws on residential leases and landlord-tenant relation in Texas. These may be supplemented by county or municipal or other local laws, which may impose additional obligations on either party. In many areas the effect of the Texas law depends on what agreements there may be between landlord and tenant, particularly the provisions of any lease.
Texas Property Code
Texas Property Code 91.001 covers notices of termination of a lease. It provides that:
(b) If a notice of termination is given under Subsection (a) and if the rent-paying period is at least one month, the tenancy terminates on whichever of the following days is the later:
(b)(1) the day given in the notice for termination; or
(b)(2) one month after the day on which the notice is given.
(d) If a tenancy terminates on a day that does not correspond to the beginning or end of a rent-paying period, the tenant is liable for rent only up to the date of termination.
(e) Subsections (a), (b), (c), and (d) do not apply if:
(e)(1) a landlord and a tenant have agreed in an instrument signed by both parties on a different period of notice to terminate the tenancy or that no notice is required; or
(e)(2) there is a breach of contract recognized by law.
A failure to remove the tenant's belonging and leave the dwelling in "broom-clean" condition may well be "a breach of contract recognized by law."
Code section 92.104 provides that:
(a) Before returning a security deposit, the landlord may deduct from the deposit damages and charges for which the tenant is legally liable under the lease or as a result of breaching the lease.
(b) The landlord may not retain any portion of a security deposit to cover normal wear and tear.
Code section 92.109 provides that:
(a) A landlord who in bad faith retains a security deposit in violation of this subchapter is liable for an amount equal to the sum of $100, three times the portion of the deposit wrongfully withheld, and the tenant’s reasonable attorney’s fees in a suit to recover the deposit.
(b) A landlord who in bad faith does not provide a written description and itemized list of damages and charges in violation of this subchapter:
(b)(1) forfeits the right to withhold any portion of the security deposit or to bring suit against the tenant for damages to the premises; and
(b)(2) is liable for the tenant’s reasonable attorney’s fees in a suit to recover the deposit.