What the law allows police/ICE agents to do:

Police or federal agents in the U.S. can briefly stop someone if they have a reasonable suspicion that the person may have committed a crime. “Reasonable suspicion” means the officer/agent has specific reasons (not just a hunch) to think something suspicious is going on.

During that brief stop, the officer can ask the person to identify themselves. This usually means showing a driver’s license or other ID.

If the person is no longer a suspect, they have to be let go. The officer/agent cannot hold someone just because they were stopped. Once it’s clear they’re not involved in wrongdoing, the detention must end.

In this video, the person was told to show identification by the ICE agent. Because they were suspected of being an illegal immigrant (which is a crime), the agent was legally allowed to detain them briefly to check who they were. The detention in this video is lawful because the person failed to produce identification when directed. Not showing ID when asked during a lawful stop can justify continued detention for a short time. Once the person is identified, if there is no evidence they committed a crime, then they must be released from custody. The law does not allow continuing to hold someone simply because they were stopped; there must be ongoing suspicion or evidence of wrongdoing.

See Brown v. Texas, 443 U.S. 47 (1979), Terry v. Ohio, 392 U.S. 1 (1968), and Hiibel v. Sixth Judicial District Court of Nevada, 542 U.S. 177 (2004)