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).  Often they fail to move out of the path of a car fast enough and their tail feathers are caught under the car wheels.

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:

No tail  

Starting to grow

Almost there