What happens after the life span of a dental crown?

Hi mabs16,
I wouldn't say the tooth has to be extracted when a crown fails. What would happen depends on the situation. Typically if a crown reaches it's life span we remove the old crown and replace it with little or no incident to the tooth. 
If there are other complicating factors (recurrent cavity, etc) sometimes the tooth may need a root canal, and in certain situations (gum disease, tooth fracture, etc) the tooth may need an extraction if it has a poor prognosis. Hope this helps!

Nothing we do in dentistry typically last forever. With that being said the average lifespan of materials can vary depending on how well you take care of it. Just because a crown has been in service for X number of years does not necessitate replacement. It is only when we can make a diagnosis of disease that warrants treatment. In other words your crown could last much longer and only when an issue arises will the decision to replacement come about. If a crown develops a problem treatment can range from a simple repair to extracting the whole tooth depending on the diagnosis.