You may be thinking of "Knock", a short story by Fredric Brown which has its own Wikipedia page. It was first published in Thrilling Wonder Stories, December 1948, which is available at the Internet Archive, as are the Dimension X and X Minus One radio adaptations.
The alien Zan are invaders who have killed all human and animal life on Earth except for a few specimens they saved for their zoo. They have never heard of natural death, and are baffled when some of their specimens die. (However, the dead specimens are animals, not humans, and there is no mention of cancer. So maybe you're thinking of another story, or maybe you're mixing up two different stories.) In the excerpt below, one of the human specimens is visited by a Zan whom he calls "George":
Walter Phelan called out, "Come in," and the door opened. It was, of course, only a Zan. It looked exactly like the other Zan; if there was any way of telling them apart, Walter hadn't found it. It was about four feet tall and it looked like nothing on Earth—nothing, that is, that had been on Earth before the Zan came here.
[. . . .]
"There is some-thing we do not un-der-stand. Two of the oth-er an-i-mals sleep and do not wake. They are cold."
"It happens in the best-regulated zoos, George. Probably not a thing wrong with them except that they're dead."
"Dead? That means stopped. But noth-ing stopped them. Each was a-lone."
Walter stared at the Zan. "Do you mean, George, that you do not know what natural death is?"
"Death is when a be-ing is killed, stopped from liv-ing."
Walter Phelan blinked. "How old are you, George?" he asked.
"Six-teen—you would not know the word. Your pla-net went a-round your sun a-bout sev-en thou-sand times. I am still young."
Walter whistled softly. "A babe in arms," he said. He thought hard for a moment. "Look, George, you've got something to learn about this planet you're on. There's a guy down here who doesn't hang around where you come from. An old man with a beard and a scythe and an hourglass. Your vibrations didn't kill him.
"What is he?"
"Call him the Grim Reaper, George. Old Man Death. Our people and animals live until somebody, Old Man Death, stops them from ticking."