Transcript for Part 5: Kayla's Sacrifice Allows ISIS Slave to Escape
There's the Christmas tree. And there's my mom on Christmas eve. Reporter: With Kayla missing now for two christmases in a row, the family's only joy came in the letters she had written in captivity. I have had many hours to think how only in your absence have I come to realize the gift that is each one of you. This is peter Edward kassig. Reporter: By then, Isis had killed the third American hostage, aid worker peter kassig. Now the only American held by Isis was Kayla. I had come to a point where our government is not going to bring Kayla home. And she was still putting all her trust in the government. This kind of thing tears people apart. I don't know how we survived but I remember the argument. "Marsha, we need to do something. They are not going to bring Kayla home." Reporter: The military option to rescue Kayla had failed. The white house had threatened prosecution if they paid ransom. And the e-mails from Isis had stopped. Nothing had worked. I know that there are some very talented hostage negotiators in the FBI that knew what they were doing. I see no evidence of their voices in these e-mails. Reporter: For example, says former FBI chief hostage negotiator Chris Voss, his former colleagues should have picked up on the use in the very first Isis e-mail of the word guest, which has special meaning in the Arab world. You have to protect and defend your guests with your life. This is something huge that they missed because they should have responded with, "No, she's not like a guest. She is a guest and she is your responsibility as a guest." Reporter: And Voss says the muellers should have been told there was a legal way to pay ransom if the ransom money might help track down the terrorists. It's been done a number of times with the department of justice understanding. Reporter: So in this case, the U.S. Could have allowed the payment of ransom to Isis for Kayla under the exception that it would help track them down and be a lure or a bait? Yes. Absolutely. Reporter: So they missed a huge opportunity? I think they did. Reporter: But the muellers had one last hope, a government in the middle east, Qatar, that had served as a go-between with terror groups in gaining the freedom of other western hostages. We went over there to the middle east and saw several high-ranking officials. And the last one we met with came into the room, and he said, "And by the way, I just talked to John Kerry and we don't pay ransom." Then he went on to say, "I don't understand you Americans. We believe if you can save one soul, it's worth trying." Reporter: Yet, the U.S. Government had just used Qatar to broker a deal for the return of American soldier Bowe bergdahl, trading five Taliban prisoners for bergdahl's freedom. The muellers say they can't understand why the U.S. Would not again use Qatar to make a deal for Kayla's freedom. You must have been crushed. Yeah. It was one of our last gasps. We try to save our daughter and our government slammed that door. We will never stop working to set our citizens free. And bring them home to their families. Reporter: A spokesman for secretary of state Kerry said he had worked hard personally to try to gain freedom for Kayla. But as dark and as hopeless as it seemed to the muellers, they did receive one piece of what was described by the FBI as good news. They told us she had been actually taken out of the prison by Abu Bakr Al baghdadi, the caliph of Isis. They believed she was with a family, that she was safe. So my thought was, "Oh, good, Kayla's able to maybe take care of the children. She's a maid." Reporter: Nothing could have been further from the truth, as the muellers later discovered. The so-called family where Kayla was safe, was, in fact, holding her for the leader of Isis, Al baghdadi. One day Kayla was taken and she came back and she went under her cover, under her blanket, and she just cried, just laid there and cried. And that's when they said, "He married her." That's the way they put it, their way of saying he raped her. So -- Reporter: But baghdadi chose her? But look at the symbolism in that. He's raping America. Reporter: Hostages with Kayla at the time say she remained defiant, and that even when she had the chance to escape, Kayla put others first. This then 13-year-old girl, a member of the yazidi tribe who wanted to be called Julia, was also being held with Kayla as an Isis slave. Translator: I told Kayla we want to escape and I asked her to come with us. She told me no, because I am American, if I escape with you, they will do everything to find us again. It is better for you to escape alone. I will stay here. Reporter: So she stayed behind? Translator: Yes, yes. Reporter: Under a full moon, Julia and another yazidi girl made their way to freedom, tearfully leaving Kayla behind. Translator: I will never forget her sacrifice. I will never forget. Reporter: Four months later, in Prescott, Arizona. My dear beautiful Kayla. I miss you and love you. Yesterday, Friday, at about yesterday, Friday, at about 10:00 A.M., we were called -- Good evening and we begin tonight with the breaking headline. He told us it was out on Twitter. Tonight Isis says that woman, Kayla Mueller, 26 years old, is dead. My eyes are clouding up, sorry. Still not believing the horrific people had lied so much and were so evil. Reporter: Precisely H Kayla was killed remained a mystery. The muellers refused to believe that Kayla was dead, until Isis a few days later, sent three photos of Kayla's body. I just kept still writing to Kayla. Hey, sweetheart, have so much to share. You, young lady, have taught me so very much. I will see you soon. Love, mom.
This transcript has been automatically generated and may not be 100% accurate.