This is the 14852nd most frequent Russian word.
повреждением
"Повреждением" means "damage" or "injury" in English.
In this sentence, 'повреждением' refers specifically to the damage that occurred to the front bumper due to the accident.
После аварии машина стояла с повреждением переднего бампера.
After the accident, the car stood with damage to the front bumper.
The word 'повреждением' is used here to describe damage as a detail about the building's roof.
Это здание оказалось древним, но с повреждением частью крыши.
This building turned out to be ancient but with damage to part of the roof.
Here, 'повреждением' relates to the medical context, specifically the damage to the ligaments mentioned in the injury.