I am very sorry to hear about Biggie's condition. Here's what I was able to find (I know surgeries can definitely end up being expensive for our lil pups):
Tracheal collapse should always be considered when a dog, especially a toy breed, starts to show signs of a chronic cough. The current method of diagnosis is usually a tracheal xray or an endoscopy or radiographic fluroscopy of the tracheal area while the dog is anesthetized. The dog should also be tested for Valley Fever and Heartworm, both of which are conditions that can cause a chronic cough. Also, congestive heart failure can sometimes be the cause of a cough.
The most common treatment for tracheal collapse is to medically manage the symptoms through weight reduction and maintenance, stress and exercise restriction, and drug therapy. A harness should also be used instead of a collar in order to avoid further pressure on the trachea area. Although none of these are a cure, most dogs can be managed quite effectively.
Common drug therapy used in treating tracheal collapse consists of antitussives, anti-inflammatories, bronchodialators, sedatives, and antibiotics. The most popular antitussives for this condition are hydrocodone or butorphanol tartrate (torbutrol). Anti-inflammatories can be helpful in minimizing airway inflammation caused by the trauma of the chronic coughing. Bronchodialators, usually theophylline based, are used to dilate the pulmonary airways which helps to decrease intrathoracic pressure during exhalation thereby hopefully decreasing the degree of tracheal collapse. Sedatives can be used in extreme cases where antitussives do not control coughing spasms and antibiotics can be used when the possibility of tracheal infection, known as bacterial tracheitis exists. Owners of dogs who suspect or know that their pet has a collapsed trachea should be working closely with a veterinarian that is familiar with the condition in order to diagnose it and determine the best course of action.
If it becomes impossible to maintain the condition medically, there are several surgeries that are available. The only one that has resulted in long-term, repeatable success is the application of an extraluminal prosthesis. The two most commonly used prostheses are the spiral prosthesis and the total ring prosthesis. Both prostheses are fabricated from a 3-ml syringe case or barrel. Which is used, the case or the barrel, depends on the size of the dog. During the surgery, the prosthesis is applied to the outside of the trachea in order to help it hold its normal cylindrical shape. The spiral prosthesis is probably the more useful of the two as it can span a much greater length of the trachea. The ring prosthesis is more like a cuff, spanning about a one centimeter area. The initial spiral prosthesis surgical procedure has been modified to maintain blood supply to the trachea during surgery in order to reduce the likelihood of the tracheal tissue dying due to interruption of blood flow. This surgery has a moderately high success rate, although it would likely be higher if the surgery option was not so often delayed until the patient was a high surgical risk.
Here's some links:
http://azlink.com/~mkk/trachea.html http://www.inno-vet.com/journals/walfocus/11/0201.html http://www.vetsurgerycentral.com/tracheal_collapse.htm http://www.barkbytes.com/bremed/yorkie.htm