When Ed Stein signed up for Medicare eight years ago, the insurance choice seemed like a no-brainer.

Mr. Stein, a Denver retiree, could choose original, fee-for-service Medicare or its private managed-care alternative, Medicare Advantage. He was a healthy and active 65-year-old, and he picked Advantage for its extra benefits.

“The price was the same, I liked the access to gyms, and the drug plan was very good,” he recalled. After a pause, he added: “Never in my wildest dreams did I think I’d be facing a crisis like the one I’m having now.”

In November, at age 72, Mr. Stein received a diagnosis of aggressive bladder cancer that would require chemotherapy and a complex surgical procedure. The doctor who he determined was the best local specialist for his condition was not in his network, so Mr. Stein decided to switch to original Medicare for 2020 — a move that would allow him to see nearly any health care provider he chose.

That was when he ran up against one of the least understood implications of selecting Advantage when you enroll in Medicare: The decision is effectively irrevocable.