That special trait has made it even more difficult for them to fathom just how a motorist could have struck her as she walked along a street in Miller in Sydney's west on Tuesday before driving away, leaving her lying on the road with a fractured skull, neck and pelvis.

Mrs Harrison, 83, who had more than 20 grandchildren and just as many great-grandchildren, was taken to Liverpool Hospital where she was admitted to the intensive care unit.

She was surrounded by family when she died from her injuries early on Wednesday.

"Everyone says their grandmother is such a sweet lady but, honestly, Nan never had anything bad to say about anyone," her grandson Daniel Webster said.

"Even in the worst person, she'd always see some kindness in their hearts. She was such a gentle, compassionate lady. It makes it so much harder that something this tragic could happen to her."

At the weekend, Mrs Harrison's family had gathered to cut a cake for her 83rd birthday. She had taken great joy in cradling her youngest great-granddaughter, Xanthe, who is nine weeks old.

Mrs Harrison had lived in the same house in Miller for more than 50 years, after migrating to Australia from England. Her husband died about 15 years ago, but she did not want to move away from the only home she had known in Australia and where her family had grown up, Mr Webster said.

One of Mrs Harrison's rituals was to wander down to the local shops, where she would sometimes have a coffee and pick up some food.

"Every day, she would go down to the shop. It was her thing to do, and people would stop and chat to her, and she would talk about her grandkids, about how much she loved her family. It was really everything to her," Mr Webster said.

Mrs Harrison was believed to have been making her regular trip to the shops when she was found lying in the middle of Shropshire Street, near the intersection of Dorset Place, in Miller, about 11.45am on Tuesday.

Police and paramedics came to her aid, but she was unable to tell them how she had been injured. Detectives say initial investigations suggest that she had been struck by a vehicle.

Mr Webster said that, if a hit-and-run driver was responsible for his grandmother's death, he hoped the driver understood the consequences of his or her actions.

"I hope they have some sort of conscience to be able to come forward. It's not going to change the fact that we've lost her now, but if they have any sort of heart, it's better for them and better for everyone to come forward," he said.

"The police should catch them sooner or later, and it would give some sort of solace to our family to know that someone that could do this could come forward."

At the time she was found, Mrs Harrison was wearing a cream short-sleeved top and a brown floral skirt and was carrying a dark shoulder bag.

Police are appealing for anyone who may have seen Mrs Harrison before she was found on the road, or who has any information about the incident, to call Green Valley police or Crime Stoppers on 1800 333 000.