The woman, who died of head injuries Tuesday, has been identified as 68-year-old Sally Katona-King.
Detectives passed out community alert fliers Tuesday at the CTA's Fullerton station. They hope more witnesses will come forward.
The offender robbed a person of an iPhone around 4:30 Monday afternoon. As the offender was making his escape, police say, he knocked a different person, the now-deceased woman, down the stairs.
"I will say that obviously since there is a death involved, we are investigating this as seriously as any homicide," said Commander Gary Yamashiroya, Chicago Police Department.
Katona-King was a deacon in her Logan Square church and a receptionist at the Lutheran Synod in Lincoln Park. She was also a mother and a grandmother.
"Everybody should be the way my mom was. It's just common courtesty. If we had respect for one another, we wouldn't be stealing iPhones," said David King, son.
"We spoke to the young woman whose iPhone was stolen from this man and she stayed with my mom, she held her until the paramedics came," said Kimberly Katona, daughter. "I was very grateful she did what she did. I'm glad my mom was not alone."
"She felt responsible, and it was not her fault," said David King.
Chicago has a seen a rash of iPhone robberies in high-profile places including Michigan Avenue. Aaron Hessel was a victim four months ago.
"One guy came up and asked me the time. I pulled it out of my pocket. As soon as I did that two other guys cornered me in a car and pulled a gun," Hessel told ABC7.
Katona-King's family and friends choose to remember the life she lead, not how she died.
"Sally was everyone's friend and made you feel that even if you were meeting her for the first time," said Bishop Wayne Miller.
"She's gonna be missed by everyone," said Leona Kerchner, friend and fellow church member.
So far, no one is in custody. Detectives tell ABC7 they have only a vague description of the suspect, but they are reviewing surveillance tape from nearby cameras.
The robbery victim was not hurt.