I frequently visit Karachi - and even though I am from Pakistan I consider myself an expat since I have lived the majority of my life outside and I am not from Karachi so it adds another layer of unfamiliarity to the situation.
Karachi is a very large metropolis - the largest in Pakistan. It has its safe parts, and it has its rough parts just like every other large city in any country.
Safety depends entirely on the area where you are staying. If its near Clifton or downtown Karachi near the major hotels, then you'll be okay. The major shopping centers and malls are also safe. Tariq road, for example is constantly busy throughout the night with shoppers.
I would caution against going anywhere else alone even for male visitors who are unfamiliar with the area.
Specifically for women - first, I would caution against traveling alone. If you must, only do so using reputable taxi companies like white cab; or arrange for a driver from your hotel (almost all can arrange a car with a driver for you).
Having not ventured into the slums I cannot comment; but on the whole there are areas of Karachi where even the locals caution against going - due to the various sectarian issues; and these ares often come up in such discussions.