In Texas, a person must generally bring suit for personal injury or property damages within two years after the day the cause of action accrues. However, an exception to this rule has been created by Texas Civil Practice and Remedies Code Section 16.061, which states that the right of action of the state or a political subdivision of the state, including a county or incorporated city or town, is not barred by the above-cited two year statute of limitations. Bryant v. Mission Municipal Hospital, 575 S.W.2d 136 (Tex.App.--Corpus Christi 1978, no writ). And, it does not matter whether the governmental entity was acting in a governmental or proprietary function. City of El Paso v. Del Norte Golf and Country Club, 614 S.W.2d 168 (Tex.App.--El Paso 1980, writ ref'd n.r.e.).
However, in subrogation lawsuits, the subrogating entity "steps into the shoes" of the insured or claimant. Since the insured or claimant would be bound by the applicable statute of limitations, it can be argued that a governmental entity pursuing subrogation should likewise be bound. However, this issue has yet to be addressed in Texas.