The surgery he had that December revealed that the cancer had spread to his liver.

“We were moving along in our relationship, and I might have asked her to move in with me,” said Mr. Olexa, recalling the period right before March 2008, when he was to about to start chemotherapy. But with the cancer, he instead asked her, “Are you going to stay or are you going to go?” he recalled. “And she looked at me like I had three heads. She said, ‘Why would I leave?’ ”

Mr. Olexa was not the first person to ask if his illness had dimmed Ms. Sclafani’s love for him, nor was he the last. (Ms. Sclafani said she was baffled every time someone raised the issue.)

“When we got the second opinion, they give you the life expectancy, it wasn’t a good one, anywhere from two to five years, and I didn’t care,” she said. “The only thing that ever crossed my mind was what can we do to help him get better or to continue his life as long as we possibly can. I was in love. I still am in love. And I was brought up that if you love someone, you love them for everything that they come with.”

More surgery followed the chemotherapy. But by August 2008 he had regained enough strength to drive. He went to a jewelry store, sold some old jewelry, then bought an engagement ring for Ms. Sclafani; he surprised her with it the following month. He made his proposal in the kitchen of her parents’ house in South Brunswick, N.J., as her parents, who knew what he had planned to do, looked on — at first in horror.

“We thought he was passing out on the tile floor,” said Mary Ellen Sclafani, who along with her husband, Guy, was sitting at a table in the room. Both jumped when they saw him moving toward the floor.

“Out of the corner of my eye, I thought Michael was falling, and it nearly scared me to death,” said Ms. Sclafani, who by then had lost her job at the Disney Store. She now works as an assistant in the pharmacy department of the Costco in Edison.