For one tortured weekend, the parents of Kayla Mueller refused to believe that their daughter was dead. From their home in Prescott, Ariz., they issued an impassioned plea to the Islamic State, which had held her captive since August 2013, and urged the extremist organization to contact them privately with proof of her death. The militants acquiesced and sent at least three photographs of her corpse.

Those photos are among the few clues about her life and death in captivity, as is a letter that she wrote from her cell last year and that her family made public on Tuesday.

Two people briefed on the family’s communication with the Islamic State said that her parents had received at least three photos. Two showed Ms. Mueller, who was 26, in a black hijab, or Muslim head covering, that partly obscured her face. Another showed her in a white burial shroud, which is used in traditional Muslim funerals. The images showed bruises on the face, but both people, who reviewed the photographs and asked not to be identified given the sensitivity of the matter, said it remained unclear whether her injuries were consistent with being killed in the rubble of a flattened building, as the Islamic State reported.

The group, also known as ISIS or ISIL, said on Twitter last week that Ms. Mueller had died in a building that had been demolished by Jordanian airstrikes, a claim that both the White House and Jordan’s government said was unfounded.

Yet the images sent to her family did not completely rule out death in that manner.

One of the two people briefed on the evidence said that Ms. Mueller’s face did not show puffiness or other concussive effects associated with a bomb blast, making it unlikely that she was killed when the area was hit, as the Islamic State said. But the same person said that she could have been in a nearby building or struck by flying debris.

American officials confirmed that the structure was bombed in coalition airstrikes last week.

The authorities insisted that the building, a weapons storage facility, was a legitimate target and explained that they had conducted detailed surveillance to make sure that no hostages were seen going in or out. But a senior American official who requested anonymity to discuss classified information acknowledged that they had not been able to survey the building around the clock.

“We have no definitive evidence of how, or when, she died,” he added.

Described by friends and family members as a deeply idealistic young woman eager to help those less fortunate, Ms. Mueller was just shy of her 25th birthday on Aug. 4, 2013, when she disappeared in the northern Syrian city of Aleppo.

She had arrived in Syria a day earlier with a Syrian man who has been described as her boyfriend or colleague.

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He had been contracted to fix the Internet connection at a Doctors Without Borders office, and employees of the international charity were flabbergasted when Ms. Mueller showed up with him.

Syria was then a no-go zone for most international aid workers, said employees of the charity, who explained that they had reluctantly housed her overnight and agreed to drive her to a bus station for what was supposed to be her trip back to Turkey.

Her car was ambushed on the way, and she and her Syrian companion were abducted. He was later freed and has declined to speak about what happened.

Once in the hands of the militants, Ms. Mueller was forced to wear the hijab and was placed in a cell with female detainees, according to two former hostages held in the same facility. She was moved a number of times, and witnesses saw her inside a potato chip factory near Aleppo and later at a prison set up on the grounds of a gas installation in Raqqa, the capital of the group’s self-declared caliphate.

While many of the male hostages were tortured, the female captives, including three staffers of Doctors Without Borders, were treated relatively well, according to a European hostage who met Ms. Mueller during his monthslong captivity last year. The women were not beaten, he said, and he said he believed that they were not sexually molested.

This seemed to be confirmed in a letter that Ms. Mueller wrote to her family last spring and that her parents released on Tuesday. On a piece of lined notebook paper, she wrote in crowded, cursive script: “Everyone, if you are receiving this letter it means I am still detained but my cellmates ... have been released.”

“Please know that I am in a safe location, completely unharmed + healthy (put on weight in fact); I have been treated w/utmost respect + kindness.”

She begged her family for forgiveness: “If you could say I have ‘suffered’ at all throughout this whole experience it is only in knowing how much suffering I have put you all through,” she wrote. “I will never ask you to forgive me as I do not deserve forgiveness.”

In Arizona, her extended family and friends gathered by the steps of the Yavapai County courthouse to ponder what had driven her to such a dangerous place. They and others described a deeply committed young woman who refused to avert her eyes from the suffering of others.

“Kayla has touched the heart of the world,” said her aunt Lori Lyon, speaking on behalf of the family.

Her desire to help solve world problems was already on display in high school, where she became involved with a campaign that aimed to stop Flagstaff, Ariz., city officials from using recycled waste water to make snow on a set of peaks considered sacred to the Hopi people. By the time she enrolled at Northern Arizona University in 2007, the Save the Peaks campaign was just one of an array of causes she was engaged with, said her former classmate Leslie Alamer, who helped set up a website honoring her friend’s legacy.

“Every time I ran into her on campus, she was organizing something, or talking about a new issue, or else inviting me to an event. She was so active,” said Ms. Alamer, 28, rattling off the causes Ms. Mueller had joined, including one that called attention to atrocities in Darfur, Sudan.

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In college, she began researching accusations of mistreatment of detainees at the military base in Guantanamo Bay, Ms. Alamer said.

After graduating in 2009, Ms. Mueller moved to India, and soon after to Israel. In 2010, she volunteered with the International Solidarity Movement in the Palestinian territories, according to Abdullah Abu Rahma, the group’s coordinator in the village of Bil’in.

He said Ms. Mueller had joined them in using nonviolent means to protest the Israeli occupation. She lived with families in East Jerusalem in order to try to prevent the demolition of their homes. On her blog, she described sleeping in front of half-destroyed homes, using her body as a shield against the bulldozers they feared were coming.

Kathleen Day, head of the United Christian ministry at Northern Arizona University, remembered how Ms. Mueller used her blog as a way to encourage her peers to get involved. She did not just write a blog post and leave it at that: She sent it to friends and family, asking them to forward it to others and to take action.

“It’s not that she’s so angelic,” Ms. Day said. “She saw things and did what she could, whatever she could, however she could.”