Godwin, a retired foundry worker, was the father of nine children and grandfather of 14, his son, Robert Godwin Jr, told the Cleveland Plain Dealer.
Smalls said if Steve Stephens, the man who is accused of murdering Godwin, is watching, she would want him to hear her son, "My daddy didn't do anything to anyone he just shot him for no reason, for no reason".
Cleveland police chief Calvin Williams confirmed one killing but said they did not know of any other victims.
She went on to describe Stephens as having been "kind and loving to me and my children", adding, "This is a very hard time for me and my family". She said Stephens was "a nice guy" who was generous to everyone.
Dozens of family, friends and community members gathered Monday evening to remember 74-year-old Robert Godwin Sr. "She's the reason why what's happened today", he said. Goodwin can be seen shielding his face with the shopping bag.
The police chief warned residents that there was a lot of misinformation doing the rounds on social media. He called the killing "senseless".
"He didn't deserve to just be picked out randomly, and then to add insult to injury, you tape it while my father is begging for his life", she said. He also fixed cars on the side to help support his family when he was working. "But we know we need to do better", Osofsky said.
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Authorities searching multiple states for a suspect in the deadly shooting of a Cleveland man say they have no idea what led up to what they say appears to be a random shooting. "He took our dad", Godwin's daughter Tammy told CNN on Monday night.
Speaking to CBS affiliate WOIO, a distraught man and a woman identified themselves as Godwin's children.
Mr Stephens turned to violence because he was angry with his ex-girlfriend Joy Lane, he says in a video posted to Facebook.
"We're still asking Steve to turn himself in, but if he doesn't we'll find him. we're not going to stop until he's in custody". The company said that Stephens posted a video of himself announcing his intent to commit murder, then two minutes later posted another video of himself shooting and killing Godwin.
Menlo Park, California-based Facebook released a timeline of events related to Stephens, something it had not done after other violent incidents.
They said they have had no contact with the suspect, Steve Stephens, since Sunday, when they tried to persuade him to surrender while talking to him on his cellphone after the shooting. "He could be far away or anywhere in between", Federal Bureau of Investigation agent Stephen Anthony said on Day 2 of the manhunt for Stephens, a 37-year-old job counselor for teens and young adults. Anyone with information is asked to call 911 or 1-800-CALL-FBI.