The two officers responding to the call did not identify themselves to Jefferson before she was killed, and there was no evidence Dean knocked on the door.
"My wife and I wanted to do something for that family", Barnes said to reporters in a video posted by NBC Sports.
According to reports, Barnes and his wife Brittany will cover more than half the cost of Jefferson's funeral, while Jackson will pay for the remainder of the expenses.
A neighbor who called police about Atatiana Jefferson's open front door before she was killed had asked officers to do a wellness check, but instead the situation was treated as an "open structure case", which experts say some officers treat as a potential burglary, according to CNN.
Dean has since been charged with murder and a grand jury was been convened. "No one should be killed during a wellness check, but the biggest thing is, anytime someone has to go through that, the last thing they you want to have to worry about is trying to come up with the money for a funeral". Fort Worth Police are investigating the shooting.
It's a bad, heartbreaking situation for Jefferson's family, and Barnes sought to make things easier on them during these trying times by paying for her funeral.
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Jefferson's funeral is reportedly scheduled for Saturday, Oct. 19.
Bishop T.D. Jakes is scheduled to deliver the eulogy and the Rev. Al Sharpton is expected to offer special remarks at the funeral service, which will be open to the public.
Both services will be held at The Potter's House in Dallas.
Jefferson's nephew told authorities that she had taken a handgun from her purse when she heard noises outside and pointed it toward the window, according to an arrest warrant released on Tuesday. Dean shot and killed Jefferson within seconds of creeping up to the property and yelling for her to put her hands up.
Jeff Halstead, a retired Fort Worth chief of police and police consultant, said there was nothing in the body camera footage released after the shooting suggests there was a crime happening. On Monday morning he joined members of Jefferson's family at a press conference covered by CNN.