He doesn’t die. On the original script, after the overture sequence, we were supposed to read that on the screen : “One of these men is a cop, and all but 1 will be dead by the end.”. And it seems quite clear that the other guys are all dead by the end
He wasn’t dead by the end of the movie, I concede that but he could have died in the police car on the way to the hospital. Knowing cops I bet they made sure Mr Pink did not have a swell ending. After all, did you see the buddy of the police that was sitting in the chair inside the warehouse? You may have missed that part because the movie did not deal much with that guy but if you watch RD again watch real close and you may see a guy in a chair getting his ear hacked off! There is even a guy doing a dance or something but its kinda hidden in the background. Its cool how QT hides little things like that in his movies!