Sometimes a person can inhale his or her own vomit, mucus, or saliva. This is very dangerous.
Usually a person will not actually draw the materials completely into the lungs. The symptoms of aspiration of foreign materials is coughing, unconsciousness, cyanosis, cardiac arrest, and cessation of breathing.
If the person begins to develop a problem the very first thing to do is to position them so they can vomit and keep an open airway. Remove all gags or bondage immediately. Sometimes the Heimlich maneuver can help to clear their airway if something is lodged within it. If they are coughing make sure to monitor them while you get emergency medical attention. I do not have enough information yet on what else might be helpful. I have heard that some people have successfully helped in this situation by plugging the victim's nose and using their own mouths to suction the airway.
There are some things that will probably lower your risk of having this happen in play. Do not gag the person you are choking. If you do gag them have a way to release the gag in a second (literally). Do not put the bottom into such tight bondage that you couldn't turn them to the side if they needed to throw up. Don't play with someone when they have a head cold. If you have a partner who gets nauseous during play it may be a good idea to stick to shorter times of asphyxiation.