When Ms. Moses returned to the nursing home, life intervened again. This time, the rabbi got sick.

She and Mr. Zeimer have not given up hopes to get hitched, as Mr. Zeimer puts it. In the meantime, he moved to a room closer to hers, and still watches television with her at night, though he leaves earlier than previously because they get tired.

As in past years, Ms. Moses talked often about her own mother and how much she missed her. Her mother had taught her so many things, but not how to be 94: how to manage a daughter who liked to take charge and a boyfriend who made her feel needed again, all set against the daily wear of aging. In this act she was on her own.

Summing up, Ms. Moses said, “If it wasn’t for the hospital I had a good year.”

Two hours south, in Voorhees, N.J., Ms. Wong asked after my mother, who turned 90 this year, and broke her hip. Did she have activities where she lived? Ms. Wong asked.

“Here you have three meals, a bedroom and then a lot of activities,” she said, describing her days in the nursing home, where she moved in 2016 to be near her daughter. “You can pass time, enjoy yourself. Usually this kind of activity is good for the elderly, but your mom is too far from this place, otherwise it’s better to come here to enjoy herself.”

Four years ago, at the start of the series, Ms. Wong had lived in a subsidized apartment near Gramercy Park in Manhattan, where she spent her days playing mah-jongg with three women from the building. The onset of dementia and consequent move to the nursing home had been very difficult for her, and this year her spirits were up and down. Though she has made new friends, she also had recurring bouts of anxiety, including one that landed her in the hospital.

“She kept telling the people they put hot water on her and burned her skin,” Ms. Wong’s daughter, Elaine Gin, said. “Delusions. Finally they sent her to the hospital. I was there at 4 or 5 o’clock in the morning. I entered the emergency-room door and I can hear her talking. She’s nice, she says, ‘Thank you very much,’ ‘You’re so nice.’ They do all the tests. She’s fine, but she’s talking and talking and talking. At 11:40 my friend came so I could go to work, and she’s still talking. They moved her to a room, and she couldn’t stay by herself. I got off early, at 4 o’clock, and she’s still talking. At 6:30 she finally calmed down. She wanted to stand up, she wanted to walk around.”

In late November she was back in the hospital, this time for dehydration and kidney malfunction. When I asked what was wrong, she said: “I think I fell down, because I am very weak. Now I can’t take very big steps.”