100% of them have a criminal record. They are in the country illegally.
Actually, only someone who has been convicted of a crime has a criminal record.
Being in the United States illegally in most cases subjects an alien to civil rather than criminal penalties—for example, deportation or "voluntary departure"* and a restriction on future admissibility. (The immigration statutes prescribe various ineligibility periods, depending on the nature and seriousness of the infraction.) One of the most common violations of the immigration law occurs when an alien stays in the United States longer than permitted by the type of visa that was used for entry.
Of course, an alien who commits a crime in the United States is subject to criminal prosecution and punishment prior to whatever immigration procedures may apply (typically deportation except in cases where a lawful permanent resident commits a minor crime).
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*A rather deceptive term, since it really means involuntary departure. This is where an alien who violated the terms of a visa is given a modest amount of time to make travel arrangements and leave the United States; the alien is responsible for the travel expenses.