Asha Grinnell prays with Su Wilson at Eastside Church in Bothell, Wash., on March 15. Wilson’s mother, Chun Liu, who has tested positive for the coronavirus, is a resident of Life Care Center of Kirkland, the Seattle-area nursing home at the center of one of the biggest coronavirus outbreaks in the United States. (David Ryder/Reuters)

The Rev. Peter Walsh has always treasured the tactile job of performing last rites for his congregants before their deaths, noticing with awe the way anointing a person with holy oil and laying his hands on their body seems to make them approach their last moments more easily.

But William Pike, a 91-year-old member of Walsh’s Episcopal church in New Canaan, Conn., was dying of the novel coronavirus.