Ending up with someone's ID during a petty theft can support a fraudulent possession of identifying information charge, even with no intent to commit identity theft.
Fraud is a broad category covering situations where one party is alleged to have misled another, usually for financial gain.
Identity theft is easier to fall into than people expect. Consider two teenagers going through unlocked cars and taking whatever is inside, including a purse or an insurance card. If they end up with someone's identification, they can be charged with fraudulent possession of identifying information, even though the actual intent was petty theft. These can become serious felony charges for someone who never set out to commit identity theft at all.
Citation: Texas Penal Code §32.51, Fraudulent Use or Possession of Identifying Information
Degree and classification: Graded by the number of items involved, from a state jail felony under 5 items up to a first-degree felony at 50 or more, with enhancements for elderly or minor victims.
Statutory language: A person commits an offense if, with intent to harm or defraud another, they obtain, possess, transfer, or use another person's identifying information without consent.