I'm new around this part of ARFCOM, so please put me back in line if I step out...
I don't know the full specifics of this call, nor do I assume to state what this person was feeling.
However, working Fire/EMS for roughly 7 years, both paid and volunteer, I've seen my share of death. I have an uncanny ability to turn off emotion that scares my wife and those who know me closely. I see it as a blessing, however, more than a curse. It's not that I don't have compassion for the situation the people are in, it's more like the emotion just cuts off when I walk on scene. I remember, when I was a sophomore in college and worked my first code, I was upset later that night b/c it DIDN'T upset me. Maybe this woman had a similar ability, maybe she had been a nurse, or was awaiting the maker to take her sister home. I hope this was the case.
However, I have seen a couple of cases that will chill anyone to the bone, where the "caretaker" cares more about the social security check or the gov't benefits that show up in the mailbox than they do the "recipient" of the check. I recall specifically one house in my town to which we'd often respond for an elderly male suffering from a hypoglaucemic diabetic emergency (low blood sugar). The sister showed absolutely no worry, fear, or concern for his obviously debilitating condition (he was a very nice man when his sugar was correct, he attacked me once while in his sugar stupor but was humbly apologetic once his levels were corrected). More disconcerting was that she was actually ANNOYED that his medical emergency disturbed her day. Her lack of concern for his medications and feeding schedules (often believed to be the cause of his lapses) went past negligence and bordered cruelty. Many of us were sure that she was just keeping him around as a cash cow.
As much as we like to hope and search for the good in people, there are evil ones about as well. I sincerely hope the woman you mentioned just felt emotionally detached from the stress of the situation, or some other good reason. I wish you the best of luck in coping with the situation... talk to a counselor or a trusted friend, take some vacation time, or maybe move into a specialty field (traffic, admin, etc) for a little while to get a different perspective... Hopefully things will adjust back to normal and you can continue on with the career you enjoy...
When I get back from Iraq I am hopefully going to move into the police field. I look forward to helping out in a new way, and seeing things from a different side of the scene. Best of luck to you!