The trachea (windpipe) is mostly cartilage and connective tissue, so it heals more slowly than most tissues. I guess it depends on how severely damaged.

Depends on how severe the damage and what caused it. Inflammation and ulceration after a medical procedure will usually heal on its own. If you sustain a severe injury to the trachea it's a different story. As the primary air canal in the vertebrate system, any damage incurred by the trachea could impair respiration. In the event of damage to the trachea, it may be necessary to undergo a procedure known as intubation. In this procedure, doctors place a tube in the nose or mouth and down to the trachea to get air to the lungs. The presence of fractures or inflammation in the trachea may require that a physician perform a tracheotomy to clear the airway. A tracheotomy, which is performed under general anesthesia, involves making a surgical incision in the throat area that creates a hole in the trachea through which a tube is inserted to provide ventilation. Inflammation of the trachea can lead to other conditions, such as tracheitis, which is the inflammation of the linings of the trachea. Tracheobronchitis occurs when the mucous membrane of the trachea and bronchi become swollen, and tracheomalacia occurs when the connective nerve tissue in the trachea degenerates. Infections to the trachea may result in what is referred to as tracheomegaly. A collapsed trachea, resulting from defects in the cartilage which makes the cartilage unable to support the trachea, results in a dry hacking cough. To detect and treat abnormalities associated with the trachea, computer tomography scans, or CT scans, may be used.