The statute of limitations for debt in Texas is four years. But if the landlord has failed to account for and return your security deposit, the landlord has a bigger problem.
A landlord who wrongfully withholds a tenant's security deposit can be liable under Texas Property Code section 92.109 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.
You can review these sections of the Property Code at the following web address:
Texas Property Code Chapter 92 - Landlord - Tenant Residential Property
The landlord has an obligation to provide an accounting for your security deposit provided that you owed no rent and had provided a forwarding address. See Property Code section 92.104. If the accounting is wrong, or you dispute the accounting, you can sue in small claims court for a wrongful withholding of your security deposit.
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