Godwin's daughter said he was killed while collecting cans in a plastic shopping bag. We are doing everything we can to help and help locate him.
She said her father, who had 10 children, was a gentle man with nothing mean about him.
Stephens also claimed publicly to have committed multiple homicides, according to police.
"Stephens is described as 6'1" and 244 pounds.
"He is considered armed and risky, so we want people to be careful out there", Williams told reporters Sunday. "If seen call 9-1-1".
When pressed about rumors that Stephens' cell phone had pinged in Pennsylvania, Chief Williams said his last confirmed location was at the murder scene. The elderly man who was shot in the video was apparently a random victim, police said. Godwin, a repairer of The Breach Ministries of Hope International Church, also mentioned to those concerned for the the family that they haven't set up a GoFundMe page for her father.
The video is likely to reignite a debate about the haunting reach of grisly violence in the Internet age and follows shocking beatings and killings shared in real time, or soon after, on a global stage.
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"We work hard to keep a safe environment on Facebook and are in touch with law enforcement in emergencies when there are direct threats to physical safety", a Facebook spokesperson said in a statement.
Chief Calvin Williams says detectives talked with Stephens by cellphone Sunday after he shot 74-year-old Robert Godwin Sr. but haven't had contact since.
He was last seen wearing a dark blue and grey or black striped polo shirt. I don't know what I'm going to do. "I encourage you to give them a call and then call us and turn yourself in".
Police and the Federal Bureau of Investigation in Cleveland said Monday that the suspect, 37-year-old Steve Stephens, could still be in the city or in surrounding states.
Police earlier had reported the victim's name as Goodwin.
In his live video, Stephens said he "snapped" and had "a lot of built-in anger and frustration". However, police said they have no evidence to support that after checking several locations. He had been working as a vocational specialist for their Assertive Community Treatment program for youth and young adults since April of 2015.
Mr Godwin did not seem to recognise the woman's name.
Beech Brook spokeswoman Nancy Kortemeyer says Monday there was nothing in the background check for 37-year-old Steve Stephens that caused any concerns.
Godwin's family members were in tears when they spoke Sunday with local reporters. "Feels like my heart is gonna stop".