Deciding not to undergo treatment for a dental problem is always an option, although it may not be in your best interest.
Untreated infections can progress to life-threatening situations, especially in immune-compromised patients like diabetics and those with AIDS. However, even among healthy persons, it is not unheard of for a patient to die of an untreated dental infection. A few situations bear specific warnings:
Failure to treat an infected tooth will ultimately lead to loss of the tooth. Loss of teeth may cause the remaining teeth to change position, changing the way they mesh in function. This can lead to overloading of the remaining teeth, and a domino effect of fractures, chips, bite collapse (loss of "vertical dimension of occlusion"), chronic facial muscle soreness and jaw joint dysfunction. In addition it can lead to improper nutrition and subsequent digestive issues. The lower face can change shape as the cheeks lose their underlying support, and the corners of the mouth may become chronically fissured and chapped.