Fredric Brown wrote a fun very short story (he was known for page-long short stories) about a scientist who discovered immortality and took the serum, but he had a cold at the time, so the bacteria also became immortal, took over his body, became pneumonia and put him in a coma. Eventually, his colleagues buried him.
Edit: Found the story. Got the details slightly wrong, but the gist was the same- fb2.top/…/part-16