Coursey told NFL Network that Adams, 26, was experiencing “health issues” Sunday, so his girlfriend called for an ambulance. Adams arrived at Self Regional Hospital in Greenwood just after 8 a.m. ET and was pronounced dead in the emergency room at 8:21 a.m.
An autopsy conducted Sunday showed Adams had an enlarged heart, a condition that Greenwood County chief deputy coroner Marcia Kelley-Clark told The Associated Press can often lead to a heart attack. But Adams' relatives didn't know about it.
"Nobody was aware of any kind of medical condition," Kelley-Clark said.
Toxicology tests are being run by the State Law Enforcement Division, though drug use isn't suspected as a factor in Adams' death. However, those results probably will not be available for "a few months," Coursey said.
The Tampa Bay Buccaneers drafted Adams fourth overall in 2007, but they traded him to the Bears on Oct. 16 for a 2010 second-round pick. Adams hadn't been able to live up to expectations that he would revive the Bucs' once-feared pass rush, having just 13.5 sacks in 37 games with the team.
Adams fell short of the benchmark set by Bucs coach Raheem Morris, who said at the start of training camp this season that the former first-round pick would be considered a "bust" if he didn't reach double digits in sacks.
Adams said during camp that he welcomed the challenge posed by Morris, who also called out the third-year pro after he began the season with lackluster performances in the first three games.
"In football, you need that," Adams said in early August. "Players tend to get in their own element and do things that they want to do. They need to be called out sometimes. He's the coach. Whatever he says, goes.
"I take it as a challenge. Being drafted fourth overall, that comes with the territory. It's year three for me. Obviously it's time for me to step up."
On Sunday, the Bucs issued a statement from Morris, who said: "Gaines will be missed by all of us, especially by his teammates in our locker room. He was a true team player and a positive influence to everyone he met. My prayers go out to his family."
"I still don't want to believe that it is true," Bucs defensive tackle Chris Hovan said in the statement. "I am deeply saddened that we have lost someone who I considered a friend for life. When he came to Tampa, I took Gaines under my wing; I considered him my little brother, and that's how I will always remember him. This is all so unreal, and it hasn't really hit me yet."
Adams played brief stints in 10 games with the Bears and made five tackles.
"Our condolences to Gaines' family, his teammates on the Bears and Buccaneers, and their organizations on their loss," NFL Commissioner Roger Goodell tweeted Sunday morning shortly after arriving in San Diego for the Jets-Chargers divisional playoff game.
Bears linebacker Brian Urlacher told the Chicago Tribune on Sunday that news of Adams' death was "crazy."
"I didn't know him that well because he came in during the middle of the season," Urlacher said. "But I did know him. I still saw him every day when I went into work. It's just weird.
"I had a teammate die when I was in college. You just don't know how to handle it. It's just sad, man. It's a bad deal."
Adams was an All-American at Clemson University and was well-known among Tigers fans for breaking up a Wake Forest field-goal try during a 2006 game and returning it for a touchdown.
Adams was the 2006 Atlantic Coast Conference Defensive Player of the Year.
Tommy Bowden, who was Adams' coach at Clemson, said he couldn't believe his former player is gone.
"I just couldn't believe it was Gaines," Bowden said. "I will always remember the smile he had on his face and I will always remember his patience."
The Associated Press contributed to this report.