I have seen cruel city... it more or less fits your requirement of a criminally-labelled character in love with a main female, but the romance hits a certain point where it sees no more development because it's not a focus for the drama or for jung shi hyun's character to pursue it.
maybe love me if you dare? I started this & I only know so much about it, but it didn't feel like something I could get into.
I don't think it's what you have in mind, but there's also boku no yabai tsuma. very gone girl within the first two eps, but it branches into its own story after that.
I can think of a few more dramas, but they don't necessarily involve a criminal falling in love with the female lead & are more along the lines of obsession, or the female isn't a main, etc.