“You got a problem, bud,” Carpenter recalled telling Tuggle after Tuggle said he was in pain.

Tuggle got his shoulder checked out at Memorial Sloan-Kettering Hospital, and Carpenter accompanied him to a meeting with his doctors. The news was not good.

Tuggle was told that he had a rare cancerous sarcoma and that the treatment would include chemotherapy. Carpenter, who had been silent to that point, whispered something to Tuggle, who then asked his doctor: “When can I put my sperm in the bank? I don’t want it affected by the chemo, and I plan on having children when this is done.”

“That positive attitude excited the doctors,” Carpenter said.

For a while, Tuggle got the upper hand on the disease. “He didn’t just keep working out,” Carpenter said. “He was making strength gains. It was amazing.”

Tuggle was one of several Giants of the era to receive a cancer diagnosis, including Karl Nelson, Doug Kotar and Dan Lloyd. “We were all aware of that and wondered what it meant,” Carpenter said, “but we were football players, trained to be tough and not be afraid.”

Tuggle went on to show his teammates new levels of toughness. He spent two more seasons with the team, inspiring others with his presence.

“We had some rough, tough, mean” players on that team, Carpenter said. He added: “But still, there was always a reason not to give 100 percent — ‘my ankle hurts,’ ‘my wife kept me up half the night,’ whatever — but when guys came off the practice field and saw him working hard, with cancer and no hair, everyone would ask, Why can’t I give my best?”

But after the 1985 season, Tuggle’s contract was up, and he was not re-signed. (Though they did not keep him on the team, the Giants paid for his health insurance for the rest of his life.) Tuggle’s daily routine was gone, and his cancer worsened, spreading to his lungs and then to his brain. And for the first time, he showed signs of weakening.