(CNN) Lawyers for the family of a transgender immigrant say she was physically abused while in US custody and died from insufficient medical care.

Roxsana Hernandez Rodriguez was an HIV-positive transgender woman who fled Honduras to seek asylum in the United States, according to lawyers representing her family.

She entered ICE custody on May 13 at the San Ysidro Port of Entry near San Diego, California, according to ICE. She was transferred to a privately run ICE detention facility, Cibola County Correctional Center in New Mexico on May 16 and housed in a unit for transgender detainees.

Nine days later, she died at Lovelace Medical Center in Albuquerque. The preliminary cause of death was identified as cardiac arrest, ICE said in a statement at the time.

But a private autopsy paid for by the Transgender Law Center, which is representing Hernandez's family, suggests she most likely died from "severe complications of dehydration" on top of HIV infection. The report also found bruising on her body that suggests she was shackled tightly at the wrists and beaten on her back and abdomen, lawyers for her family said.

"Her death was entirely preventable," said Lynly Egyes, director of litigation for the Transgender Law Center, in a statement Monday. TLC sent a written notice of a personal injury and wrongful death claim to the state of New Mexico on November 19, the first step in filing a lawsuit.

US Immigration and Customs Enforcement said in a statement that it could not speak to the validity of the private autopsy, which was first reported Monday by the Daily Beast.

"However, allegations that she was abused in ICE custody are false," the statement said. "A review of Hernandez's death conducted by ICE Health Service Corps medical professionals confirmed that she suffered from a history of untreated HIV. At no time did the medical personnel treating Ms. Hernandez at Cibola General Hospital or Lovelace Medical Center raise any issues of suspected physical abuse."

A spokeswoman for CoreCivic, which manages the Cibola facility, said that Hernandez was detained at Cibola for only 12 hours before she was transported to an outside hospital on May 17.

"We take the health and well-being of those entrusted to our care very seriously. Whenever there is a death in custody, CoreCivic immediately notifies our government partners and all appropriate authorities with oversight responsibility. We cooperate fully with those investigations," Amanda Gilchrist, director of public affairs, said in a statement.

Hernandez was one of roughly 25 transgender and gender-nonconforming individuals who joined the annual caravan of Central American migrants heading to the US border organized by Pueblo Sin Fronteras.

Hernandez left her native country of Honduras to flee the "violence, hate, stigma, and vulnerability" she suffered as a transgender woman, Pueblo Sin Fronteras said in a statement in May.

It was a trip she had made at least three times before. She entered the country illegally twice between 2005 and 2009, and was granted voluntary return to Mexico after claiming she was Mexican, ICE said. In 2014, Hernandez entered the US for a third time and was deported shortly after, according to ICE.

Yet, she set out again this year in April.

"She saw in the United States the opportunity to start new life free of abuse, risk, and threats, by seeking asylum," Pueblo Sin Fronteras said in May.

Lawyers say her condition began to deteriorate as soon as she entered US Customs and Border Protection custody in San Diego. She grew ill in the notoriously cold holding areas known as "hieleras," or "coolers," TLC says in a press release.

She was denied access to requested medical care, the lawyers say, and only saw a doctor after days of vomiting and diarrhea.

Lawyers say the neglect continued after she was transferred to Cibola on May 16.

"Forensic evidence indicates she was handcuffed so tightly as to cause deep tissue bruising and struck repeatedly on the back and rib cage by an asp or similar instrument while her hands were restrained behind her back," the lawyers say in their written notice.

On May 17, she was admitted to Cibola General Hospital with symptoms of pneumonia, dehydration and complications associated with HIV, according to ICE. Later in the day she was transferred via air ambulance to Lovelace Medical Center, where she remained in the intensive care unit. Staff pronounced her dead on May 25, ICE said.

"ICE takes very seriously the health, safety and welfare of those in our care, including those who come into ICE custody with prior medical conditions or who have never before received appropriate medical care," the agency said in a statement Monday. "Any death that happens in ICE custody is a cause for concern, and the agency will continue its full review of this case according to standard protocols."

Gilchrist said that CoreCivic's ICE-contracted facilities are contractually required and held accountable to federal Performance-Based National Detention Standards, "which include guidelines for the safe and appropriate accommodation of transgender detainees."

Officers are required to complete 160 hours of pre-service training and ongoing annual training, she said. The training includes the dynamics of sexual abuse and harassment and guidance on respectful interactions with lesbian, gay, bisexual, transgender, intersex and gender-nonconforming detainees.