As the authorities work to identify the immigrants who died in an overheated tractor-trailer in Texas and investigate the smuggling network that put them there, attention is now turning to another complicated question: What happens to the survivors?

Eight immigrants who were trying to sneak into the United States were found dead on Sunday morning after the truck parked in a Walmart lot in San Antonio, and two died later.

The 29 who survived could be candidates for deportation. But in the past, bearing witness to such a gruesome event has proved to be a perverse kind of blessing by helping some immigrants achieve their initial goal: a life in the United States.

Under programs meant to help prosecutors build better cases, the authorities can offer protection from deportation, and even a path to potential citizenship, to immigrants in exchange for testimony against their smugglers. Some advocates and lawyers are hoping that will happen. But on Tuesday, federal authorities said that a decision was still a long way off.

“Our focus right now is the criminal investigation,” said Shane Folden, the special agent in charge for Homeland Security Investigations in San Antonio.

Smuggling cases are complex, with agents trying to unspool webs of co-conspirators, which can include recruiters, organizers and people who act as guides, as well as those who maintain “stash houses” and other stopping points along the way.

The driver of the truck, James M. Bradley Jr., 60, of Clearwater, Fla., is in jail facing smuggling charges. But Mr. Folden said he hoped the investigation would lead to many more arrests and reach into higher echelons of smuggling rings.

That goal may require testimony from survivors, who can provide information such as phone numbers and descriptions of the people who brought them to the United States.

An initial hurdle for those seeking to stay is to be designated as a “material witness.” Immigration authorities said on Wednesday that 12 people remained in hospitals, and that one had escaped after checking out of a hospital.

At least 13 others have been released from hospitals and are being detained. For now, all are being considered material witnesses, though it is not necessarily a permanent designation.

“That’s probably the most prudent thing at this point,” said Michael J. Wynne, who spent 12 years as a federal prosecutor in South Texas. “Label them all material witness to stall the deportation proceedings and sort that out later.”

Most of those in the truck were from Mexico, and some were from Guatemala. One has been identified as Frank G. Fuentes, 19, who was born in Guatemala, grew up in Virginia and was deported this year after having been convicted of assault and grand larceny.

For the survivors, another key determination is whether they were smuggled into the country on their own accord, or trafficked against their will or under false pretenses.

Trafficking victims can be eligible for a range of benefits, including financial assistance, housing and psychological services, said John Torres, who worked for 26 years as a federal immigration agent. By contrast, Mr. Torres said, people who are smuggled are considered to have entered into contracts with their smugglers, which is itself a crime.

“They are probably conducting interviews now to determine whether it’s one or both,” Mr. Torres said.

There is another potential hang-up. The applications for some of the visas available to witnesses of crimes require a letter of verification, from either the Justice Department or immigration authorities, vouching for the importance of the testimony, and sometimes those agencies disagree about whether a letter should be provided.

“Some of the worst fights I have seen in my professional life have been between heads of government agencies over witnesses,” Mr. Wynne said. Prosecutors, he said, tend to want to keep witnesses in the United States as long as possible, whereas Homeland Security officials dislike what they perceive as rewarding people for violating the law.

Offering protection from deportation can backfire on prosecutors, because a smuggler’s defense lawyer is likely to use it when cross-examining victims at trial.

“A defense attorney could make the argument that, ‘Hey, they are buying you food, buying you clothes — aren’t you just making this up so that you get to stay here?’” Mr. Torres said.

There is risk for the witnesses, too: retaliation against them or their family abroad for testifying.

The question of whether the survivors in this case receive government protection may take months or years to resolve, but Michael McCrum, a San Antonio lawyer and former federal prosecutor who is representing the 13 material witnesses, said he was already pushing to make sure his clients were “adequately taken care of, and not just political footballs in our current climate of immigration angst.”