Parents should instruct and remind children to never follow or go someplace with a stranger, even when that stranger claims to know or be acting on instructions from known caregivers. Even if a stranger offers children money or something desirable, and even if the stranger asks children for help, children should be taught to yell, "NO," as loudly as they can and run away to the nearest known and trusted adult.
It is not enough to simply tell children what to do; parents should role-play such interactions with children on several occasions so as to help give them a realistic appreciation of what the actual situation might look and feel like.
In all likelihood, most strangers who might interact with children won't actually pose a threat to them, and so there is a strong element of over-correction in this advice. However, the advice is offered from a "better safe than sorry" perspective. Children simply do not have the maturity of judgment required to reliably evaluate the actual level of danger inherent in such situations, and so benefit from straight-forward, black and white instruction as to how to handle them. The prospect of hurting the feelings of an honest stranger is less troubling than the prospect of a child who comes into the hands of a predator.
Parents should not label children's jackets, backpacks, or clothing in a manner where their names become visible to strangers. Potential predators can use their knowledge of a child's name to mimic familiarity with the child (or the child's family) and so manipulate them (in the manner of a con-artist) to gain their trust. For example, a stranger can see Janelle's name embroidered on her bag as she's walking past a store. The stranger says, "Hey Janelle, I'm a friend of your Mom's. I know she says you have pretty good taste in clothes. Could you help me pick out an outfit for my niece?" Because this stranger used Janelle's name, Janelle may think that her Mom has approved of this unscheduled shopping trip and go off with the stranger.
More information on how parents and caregivers can protect their young children from child abuse, both from strangers and from known friends and family, can be found in our Child Abuse Prevention section.