Pigeons will lose a lot of feathers if they are caught by predators or hit by a car, most often those from the back, the tail and/or the flight feathers from the wings (these are the long ones at the end of the wings).
Sometimes (especially if they lose flight feathers) they will be unable to fly. However, the feathers will grow back within 6 weeks and if the pigeon is kept safe it will soon be releasable.
These photos show the progress of a young pigeon that had lost her tail feathers:
Starting to grow
Pigeons will usually moult their feathers every year, between mid July and mid December, to replace their damaged or worn plumage and to ensure that they retain their ability to keep warm, dry and to fly with agility.
The feathers are usually moulted in a particular order and it is done unobtrusively. You might notice the occasional flight or tail feather on the ground, or a number of soft white down feathers being blown about, but unless you look closely you won't usually notice much difference on wild or feral pigeons.
However, you will occasionally see a pigeon with large bare patches on the head or the neck. This isn't due to disease or parasites but is most likely a pigeon that has been bullied and pecked at when his smaller feathers were loosened by the moult. The feathers will grow back, but a good healthy diet help them devlop healthy new feathers.