For two days this week, the fate of Luis Manuel Rivas Velásquez was a harrowing mystery.

Imprisoned at the immigration detention center in the Florida Everglades known as Alligator Alcatraz, Mr. Rivas had not made his usual daily call to his sister in Venezuela. And detainees started telling their families that they had seen Mr. Rivas unconscious, receiving CPR.

After Mr. Rivas’s sister started a social media campaign, the Department of Homeland Security announced late Wednesday that Mr. Rivas was alive. He had “fainted,” a spokeswoman said.

But according to accounts from detainees, Mr. Rivas, who came from Venezuela, was in much more serious condition. Mr. Rivas, 38, was unconscious on the cell floor, with guards seeming to not know how to take his pulse, according to a recording of a conversation with a detainee, Mr. Rivas and Mr. Rivas’s lawyer that was obtained by The New York Times.

The accounts raise questions about medical care and treatment at the detention center, one of many unknowns regarding its day-to-day operations. Florida officials have defended the center, the first run by a state for federal immigration detainees, as an example of how a state can swiftly try to assist the Trump administration with its crackdown on illegal immigration. Other states have said they plan to follow a similar model.

But Everglades detainees say poor conditions at the center have persisted, and federal judges have had to pry information out of the government regarding basic matters. On Thursday, a federal judge ordered a two-week halt to further construction at the facility, pending the completion of a hearing in a lawsuit filed by environmentalists seeking to protect the Everglades.

Rumors about a serious medical episode at the detention center began on Tuesday night. Two separate recordings of phone conversations from the center circulated among Miami immigration activists, state lawmakers and journalists. In the conversations, detainees told their relatives that they had seen one or two unresponsive men inside the center. They worried that at least one of them had died.

By Wednesday morning, questions from the news media and state lawmakers prompted the Florida Division of Emergency Management, which runs the facility, to declare that the rumors about deaths were false. “There have been no life-threatening medical incidents or deaths,” Stephanie Hartman, a spokeswoman for the division, said in a statement.

That day, however, Mr. Rivas failed to call his sister, Ada Velásquez, she said in an interview.

Her alarm grew, she said, after the wife of another detainee called to share that her husband had seen Mr. Rivas receiving cardiopulmonary resuscitation.

Her husband had described the dramatic scene in detail, the wife said in an interview with The Times on Friday. She declined to be identified for fear of making her husband’s presence at the Everglades detention center known to his sick mother.

Her husband told her, she said, that guards had taken Mr. Rivas away as if he were dead. The fact that Mr. Rivas was alive, she added, may have been because a detainee had been a nurse in Cuba and knew how to administer CPR.

A second account came from a recorded conversation on Thursday with Mr. Rivas; his lawyer, Eric Lee; and a second detainee, a Cuban man who did not identify himself.

On the recording, not previously made public, the Cuban detainee described seeing Mr. Rivas unconscious on his bunk after having flulike symptoms.

Three detainees dragged Mr. Rivas to the door of the group cell, the Cuban detainee said. “They left him lying on the floor,” he said of the guards. “They didn’t even know how to take his pulse.”

At one point, a guard tried to give Mr. Rivas water, but the Cuban detainee said he had told him to stop, fearing that Mr. Rivas could suffocate. After about half an hour, Mr. Rivas was wheeled away on a stretcher, the Cuban detainee said.

The detainee said, “Everyone is getting sick.”

Mr. Rivas had been in the U.S. for about a year, according to his sister, before she had helped bail him out of a Miami-Dade County jail. Homeland Security said that Mr. Rivas had “a rap sheet that includes an arrest for robbery in Miami.” He had been detained in the Everglades since late July.

His case garnered social media attention, in part because Ms. Velásquez posted an Instagram video pleading for her brother’s body. Mr. Rivas, who describes himself as a master of ceremonies for automobile events who posts frequently about cars, has more than 250,000 followers on the platform.

Ms. Velásquez received fierce criticism for posting that her brother was dead. Yet, she said, that led Homeland Security to state that Mr. Rivas was alive.

Late on Wednesday, Ms. McLaughlin, the Homeland Security spokeswoman, said that Mr. Rivas had “fainted and was taken to the hospital out of precaution.”

“ICE takes its commitment to protecting those in its custody very seriously,” she added. “We ensure illegal aliens have access to adequate medical care.” Her office did not respond on Friday to a request for further comment about his case.

The Florida Division of Emergency Management did not respond to a request for comment on Friday regarding Mr. Rivas’s case or health conditions inside the detention center.

On his lawyer’s recording, Mr. Rivas sounded winded and congested but said that he was feeling a little better. The source of his illness is still unclear. Mr. Rivas asked for his medical record but was denied, his lawyer said, adding that he was told he had a “respiratory infection.”

Mr. Lee said that his client had signed self-deportation papers at the detention center earlier this week, before his medical episode.

“All he wants to do is go back to Venezuela,” Mr. Lee said. “There’s no reason whatsoever for him not to be let out.”

Mr. Rivas had said he would call his sister on Friday morning. As of Friday evening, neither his sister nor his lawyer had heard from him.

Alain Delaquérière contributed research.