Catherine Quintana’s father had been in and out of a hospital for weeks, and the family understood that his time was running out.

Her 78-year-old father, Ernest Quintana, had lung disease and was struggling to breathe on his own. On March 3, he was admitted to a Kaiser Permanente hospital in Fremont, Calif., for the third time in 15 days, Ms. Quintana said. He had his wife of nearly six decades and other members of his family at his side.

While they awaited the results of a CT scan, Ms. Quintana, 54, and her mother decided they would quickly go home to shower. Ms. Quintana’s daughter Annalisia Wilharm stayed at his bedside.

Ms. Wilharm, 33, said a tall machine on wheels eventually rolled into the room. Attached was a screen streaming a live video of a doctor wearing a headset.