The 23-year-old Haywood passed away at Medical Center of Arlington at 3:27 p.m. (CDT) from an undisclosed illness.
Hospital spokeswoman Diane Stout told The Associated Press, ``The cause of death at this time is unknown." She said she doesn't know what Haywood was being treated for.
Haywood reportedly woke up early Saturday morning around 4 a.m. after vomiting in his sleep. Around 6 a.m., he stopped breathing and was rushed to the hospital.
"This is a time to offer support and our deepest sympathy to the family," said Cowboys owner Jerry Jones, who spent most of Sunday at the hospital with Haywood's family. "Our hearts go out to them. This is a tragedy involving a person who was very well-liked and respected by anyone who had the opportunity to know him."
Like Jones, Haywood's teammates remain in disbelief.
"It's such a shock because I talked to him every single day," Cowboys offensive tackle Flozell Adams said Sunday night. "I just talked to him on Thursday and everything was fine.
"Every time I talked to him, he was never negative and always spirited. I know he was so excited about this season. He was in the weight room a lot and just getting ready. He kept saying this was going to be his year."
Haywood, a local Dallas product from Carter High School, competed in the Cowboys' three-day mini-camp last weekend at Valley Ranch and was expected to compete for a backup running job position this summer in training camp. A four-year letterman at Iowa State, Haywood spent his rookie season on the Cowboys' practice squad, after leading the team in rushing during the preseason with 121 yards on 31 carries.
Haywood ranks fifth in career rushing at Iowa State with 2,862 yards, and sixth in touchdowns with 27. As a senior, he ran for 1,169 yards and 14 touchdowns to lead the Big 12.
``Like everyone in the Cyclones' football family, we are shocked and saddened beyond words,'' Iowa State head coach Dan McCarney said Sunday. ``Ennis was one of the classiest gentlemen there has ever been, on and off the field. He was an unbelievable competitor, and one of the most tenacious football players I've ever been around.''
Iowa State running backs coach Tony Alford recruited Haywood out of Dallas Carter in 1998.
"Ennis was like a son to my wife Tina and I," Alford said of Haywood, a Doak Walker Award semifinalist in 2001. "He was the toughest player I have ever coached. Ennis always had a smile for you. He was a great kid and I was lucky to have known him. Coaches teach players but some players also teach coaches. I grew as a coach while I was able to teach him."
Haywood is survived by his wife Crystal and one daughter. Funeral arrangements are pending.