South Korea has low crime rates and is relatively safe country. Apparently South Koreans even leave their bag unattended in public without fear of it being stolen. Kimchi Man says he would never do that himself but he confirms it truly is a common occurrence. However, a lone woman in a foreign country might face certain dangers no matter how safe the country is.
That being said, internet seems to be full of experiences of women traveling or living solo in Korea and having a good time. Here are some we found.