Could a dental crown cause the root underneath it to die?

No: Typically the reason a tooth needs crown treatment is as the result of extensive decay or tooth breakdown that necessitates that repair. So it is that extensive breakdown that is at play if the pulp deteriorates, not the crown.

No: The crown usually does not cause this. However decay underneath the crown or a fractured tooth can cause the nerve in the tooth root to become necrotic or die.

Not necessarily: It's rare, but can happen. The act of reducing the tooth for a dental crown can be traumatic for the nerve of the tooth. Dentists are trained to control most factors affecting the nerve of the tooth during the procedure, like using copious amounts of water, but sometimes, the tooth simply will not react well, and the nerve may end up dying. This may take from a few weeks to a few years to develop.

Tooth crown: Crowns are made to restore a tooth that's decayed or broken. It's done to protect the tooth and make the tooth functional. So it saves the tooth as opposed to damage it. However, if a tooth with crown is not taken care of properly it will decay underneath the crown. The decay will gradually penetrate into the tooth structure and causes necrosis of the pulp (the tooth nerve dies).

Crown=restoration: A crown restores a tooth. It is restored from it's broken, decayed or damaged condition. Anytime a tooth is damaged it can start a process (pulpitis), that could eventually cause the nerve to die and require a root canal treatment.

No: Dental crowns do not cause the nerves of the teeth to die. Caries (cavities), occlusal trauma, periodontal disease, fractures, traumatic injuries, incompetent dentistry, and failing to see your dentist on a regular basis and not getting all your needed dental treatment can cause the nerves to die. Proper dental treatment by a qualified dentist preserves teeth, gums, bone and a healthy mouth\body.

Sometimes.: While extensive "decay" and deeply cracked tooth structure are most often the rational for a full coverage crown, the preparation / reduction of tooth structure for these issues can in itself irreversibly damage the tooth's nerve thereby necessitating a "root canal." this is especially evident when a "virgin tooth" needs root canal after being prepped as a supporting abutment for "bridgework.".