Team physician Dr. Walter Lowe issued a statement Thursday that said the injury suffered by Hayden results in death 95 percent of the time.
Hayden collided with a teammate during the practice session, tearing the large vein that carries blood from the lower half of the body to the heart.
"This injury has never been seen or reported in association with a football injury and is more associated with high-speed motor vehicle injuries," Lowe said in his statement. "The type of injury D.J. had is 95 percent fatal and we are all very thankful for the coordinate response from the University of Houston trainers, EMS paramedics, the trauma team at Memorial Hermann Hospital and operating surgeon Dr. John Holcomb."
Hayden has started all year for the Cougars, who have a 4-5 record, and has recorded four interceptions.
"D.J. is a tremendous young man and has been a great asset to our program, both on and off the field," Houston Coach Tony Levine said. "I ask that everyone continue to keep D.J. and his family in their thoughts and prayers.
"We are very fortunate to have some of the nation's top physicians and medical facilities just minutes away from our campus and I would like to extend our appreciation for their efforts on Tuesday evening. We look forward to supporting D.J. on his road to recovery."