Part of the analysis for your question depends on whether or not the landlord installed the security devices required under the Texas Property Code, and whether or not those security devices could have prevented the break in.
Under Chapter 92 of the Texas Property Code, the landlord has the obligation to provide certain specified security devices for the rental property. See for example, section 92.151, and section 92.153. The tenant may request additional security devices under section 92.157. The landlord has an obligation to repair or replace broken or defective security devices under section 92.158.
In general, if the landlord complied with its security device obligations, and did not otherwise contribute to the break in or have reason to know that the break in was likely to occur, then the landlord should be free from liability. But, an inventive plaintiff's attorney could try to create liability through a knew or should have known argument.
Typically, damage or loss from theft is covered by insurance. A prudent landlord would encourage its tenants to purchase insurance, and advise them that the landlord does not carry insurance for loss of the tenants' property or contents. That way, the landlord can point out that the tenant made the decision to buy or not to buy insurance.
You can review the landlord - tenant provisions of the Texas Property Code at the following web links:
Texas Property Code Chapter 92 - Landlord - Tenant Residential Property
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