Andrew Walls may have been pushed, police said, from a stairwell in the 7700-block of South Halsted in the Auburn-Gresham neighborhood on Tuesday night.
"He is still somebody's grandfather. He may still be someone's father. And he's still person. And to the person that did this crime he needs to turn himself in because you can't live with it on your conscience," community activist Andrew Holmes said.
Walls, a Navy veteran, encountered a robber who had just stolen someone's wallet, police said, and struggled with the offender before falling down the landing.
Walls lives at St. Leo Residence for Veterans, a seven-year-old institution run by Catholic Charities.
"It was a surprise that we heard what had happened to him. He is not an aggressive person. I don't know why he was there at that time, but maybe somebody was helping him and he was deceived some kind of way," Maurice Madison, Air Force veteran, said.
"He is just a loving person and I just don't understand how a person could do that to him," Regina Lowe, Air Force veteran, said.
Walls was rushed to Advocate Christ Medical Center in Oak Lawn. He has a fractured skull and is in critical condition.
Chicago police are investigating. While the building where the incident took place has cameras, the property manager said they were not working.
The cameras weren't working at the building, according to a property manager.