Yes the root canal treatment can be done through the crown. So this is a failed root canal that has to be retreated. Normally we drill through the crown and re-treat the root canal. It is normal not to remove any structure incase it breaks. Then one the root canal has been retreated we place a new crown on top. If you have a failed root canal you will probably have terrible pain and will need to see an emergency dentist as soon as possible.
However if the dentist can remove the crown he/she will, as long as he can do it without damaging existing structure. Normally in most instances a new crown is needed due to the fact the structure and integrity of the crown will have been changed or may be compromised. A new crown will usually be placed.
If everything fails then it is time to have the tooth removed and have a dental implant. Read more here about dental implants if you are looking for dental implants in nyc and would like to learn more.