I believe that if those lay ministers taking Communion receive the message that the sick person would like to go to Confession, that they immediately notify the priest.
Also the priest is notified if the patient is near death and asks to receive the Annointing of the Sick (what we used to called Extreme Unction.)
The Orthodox have always used the term "Annointing of the Sick". I was aware of the difference in terminology but wasn't aware that the Roman Catholic Church had changed theirs.