Curly Howard did not die while working. He did have a massive stroke while working on a short called HALF WITS HOLLIDAY, when he strangely disappears at the end and is not involved in the ensuing pie fight. Curly had to quit the Stooges but did do a cameo in a later film and it is very evident he is paralyzed on one side. They tried to have Curly play a cook in the film MALICE IN THE PALACE, but Curly was too far gone and the footage was ditched. Curly had several more strokes until he died in 1952.
Around a year before Curly left the Stooges, Curly had a stroke and if you see teh dozen or so films made after that you can hardly tell he's Curly. He looks like Shemp with a shaved head and could no longer do his falsetto. He just drags himself around eschewing any physical gags and it is heartbreaking to see.
"Everybody is born, and everybody dies. Being born wasn't so bad , was it?"
Peter the Hermit