Ms. Schafer, 46, lived in Dundee. She had spent her 18-year career with the U.S. Postal Service here, said Ed Moore, a spokesman for the Detroit district.
"We're still dealing with the shock in stages," Mr. Moore said. "This is truly just a tragic situation for all involved. Her fellow employees are suffering, but they are out there delivering mail today."
He added that some kind of official memorial service would probably be held, but no date had been set.
Yvonne Ballestri, the Dundee postmaster, said she and her staff were not commenting to the press "because of the sensitivity of the subject."
Ms. Schafer died in a freak accident shortly after 2 p.m. Tuesday while delivering mail to a home at Midway and Adams streets.
She fell about 10 feet through the concrete floor of the home's porch, then was struck by a 4-inch slab of concrete that dropped on her.
She was talking to a co-worker on her cell phone when she fell and cried for help.
Dundee police estimated the piece of concrete weighed 500 pounds.
Ms. Schafer is remembered at the Dundee village offices as a diligent letter carrier who arrived with her mail between 9:30 and 10 a.m.
"She was very friendly, very kind, and talkative," said clerk Kathy Clark. "She was always smiling."
Ms. Clark said her home was on Ms. Schafer's route and "my daughter loved seeing her come."
No charges will be filed against the owner of the property where Ms. Schafer died. He was not home at the time of the accident.
The Wayne County Medical Examiner's Office was to have done an autopsy Wednesday, but did not return phone calls.
Dundee police Chief David Uhl said he did not expect to get any preliminary autopsy results for a couple of days.
Sgt. Tom Redmond, who investigated the fatal accident, said he expected Ms. Schafer died of asphyxiation from being unable to breathe because of the weight of the concrete on her chest.