Will life insurance pay out if the death was a suicide one year after the policy was purchased?

Here is the direct answer, and it is narrower than people expect. Texas law lets a life insurance policy provide for a settlement that is less than the face amount if the death is by the insured's own hand [1]. The statute says that whether the insured was sane or insane [1]. And the statute names no time period at all. It does not say that one year, or thirteen months, or any other mark changes that [1]. So the law itself does not answer your question with a date. The words that could set a period are in your own policy, and these sources do not quote them.

There is a second Texas rule with a two-year mark, and it is worth reading carefully. A life policy must provide that a policy in force for two years from its date of issue, during the lifetime of the insured, is incontestable [2]. The exception named in the statute is nonpayment of premiums [2]. These sources do not say how that rule and the suicide provision above fit together. So do not read the two-year mark as a promise about a suicide claim.

What that leaves you with is the policy itself. Find the part headed suicide, or exclusions, and read the period it names. These sources give no day count, so your policy's own wording is where the period comes from, if there is one. Texas is also only one state here, and another state writes its own statute.

Find the word suicide in your policy, and read the sentence around it. Then compare the date of issue with the date of death [2]. Then check whether the company's letter names a policy provision or a statute. Whether your own policy limits that clause to a period: "Don't know yet" here, because these sources do not quote policy wording.