A celebrity-backed ping-pong bar isn’t where you would expect seniors to hang out. But Carol Klenfner, 72, is a regular at Spin, the New York City table-tennis club founded by Susan Sarandon.

In 2009, after a 35-year marriage and 45 years working in an office, she found herself alone. She had just lost her ailing husband and was unexpectedly laid off from her job at a public relations firm.

Forced...