Despite the low wage, this is still vital work. According to a 2018 AARP Foundation survey, roughly one-third of older adults in the United States are socially isolated, a state that is linked to increased health risks, including heart disease, cancer, depression, diabetes and suicide. Vivek Murthy, the former United States surgeon general, has written that loneliness and social isolation are “associated with a reduction in life span similar to that caused by smoking 15 cigarettes a day.”

And the problem has an impact on the health care system. Last year, there were thousands of emergency room visits in Dallas that had nothing to do with physical ailments at all. The patients were just completely socially isolated, without anyone to turn to for help.

“Loneliness is now finally being recognized as a disease, not only at a personal level, but also from a health care perspective,” said Andrew Parker, 32, who founded Papa in 2018.

His company is one of several that aims to be a stopgap, and health insurers who may be looking to cut costs have begun to take notice.

Mr. Rodger’s family is paying for Papa because of a conundrum: Mr. Rodger’s granddaughter Tanya Martin had been his primary caretaker for more than four years. But once Mr. Rodger needed dialysis, it became too much for her to handle with her full-time job as an airplane mechanic.

He didn’t qualify to have further assistance covered by his health insurance, but he also couldn’t afford a private caretaker, which can cost about $300 a day in Los Angeles, according to the prices Ms. Martin was quoted.