About a year ago my former boss, a middle-aged woman with a petite frame, was walking along V.Luna when some men in a white Corolla snatched her handbag. Unfortunately, since the strap of the bag was intertwined with her arm, she was unable to let go of the bag; this resulted in her being dragged for several meters before she managed to wrestle her arm free.
You should still consider yourself fortunate, gretzy. My former boss had to undergo an operation for a fractured hip bone, and she still walks with a crutch to this day.
And to answer your question on what places remain safe: Safety comes from prudence, from constant awareness of your surroundings, and from having the skill to respond to dangerous situations.