Teeth are a very special kind of organ. Half way between a bone and some connective tissue, teeth are living little organisms, or can be thought of as self contained little ecological systems. Like the analogy implies, teeth are alive, and they can die. But because they are so hard, and so resistant, they can stick around for quite some time after they die. A dead tooth can fulfill the functions it did in its life for years to come, if it is properly maintained.
How to tell if teeth are dead
Dead teeth are different from living teeth in that they are no longer connected to the dental nerve and have no feeling, and are no longer being nourished. This means that they no longer pick up and use nutrients and minerals from the body, and just slowly decay and atrophy over time. Since minerals are not being used, the tooth will slowly start to become discolored; it turns grey naturally as the minerals that make up the tooth enamel are drained and leached by the bacteria and their acidic by products, and can turn yellow if the enamel is gone and the cementum shows, but this too will turn grey or even black with time. Not being connected to the dental nerve also means that the tooth is unresponsive, does not hurt, and is not sensitive to being tapped. These teeth can become infected, and the pain may radiate to the teeth next to them, so pain cannot always be avoided, even though the tooth itself is dead.
Cleaning dead teeth
The way you care for dead teeth is the same as for living teeth. Floss around them and bush their surfaces, and they should be fine. They will remain intact for a long time, sometime years before they inevitably break from lack of minerals keeping them together. They can even be internally bleached so that they appear like living teeth for longer.
What happens to dead teeth
If proper oral hygiene is maintained, the tooth should not contract an infection, it is not inevitable that dead teeth necessarily become infected. They do get whittled down from daily use, and they start to crack and break, until entire pieces of tooth go missing, and eventually the tooth just breaks. The internal structures will become exposed, but this will rarely hurt, as the tooth will already be dead and unresponsive. Then more little pieces of tooth will break off as time goes by, leaving nothing in the end. When this happens, you should get the tooth extracted, and get a dental implant put in. A dead tooth can give time to save up for a dental implant, as one will necessarily be needed once the tooth starts to break, which it will soon enough. Use this time to put aside some money and some time for this procedure.