In my experience, patients rarely die in the ED. The majority come in mostly or completely dead, some are stabilized long enough to make it to the unit or the OR, and a very small number truly die in front of you. I always remember the later. At least in this case the woman lived a long life, and died with family at the bedside, even if it was in a busy emergency department and not in the comfort of her home.
After a few years of working in emergency medicine, I still find these experiences among the most difficult to deal with. I know that she was not in pain, and that her family was present, but in an environment where we're always trying to "do something," simply standing by and letting nature take its course can leave me profoundly sad, even if it is the right thing to do.
Maybe it was some sort of karma when, later that same shift, I was asked to bring a very pregnant woman up to maternity. Already contracting and getting ready to pop, Mom smiled while Dad proudly shared the name of his soon-to-arrive firstborn son. I'm not a big, circle of life kind of guy, but it was a nice ending to a long day.