The latest Snapchat feature allows users to send their friend’s Snapchat stories to each other. We are still testing to see if anyone can see these stories. We are also trying to determine if there is a notification that a user receives if their story is sent to someone privately. At the present time, it does not looks as if a user gets any notification. This means that your public Snapchat story could be seen by almost anyone and you would never know!
UPDATE: If you are not friends with someone and their Snapchat is private, you cannot see their Snapchat story even if it is sent to you. You can add them as a friend, but you cannot see their story until they accept your friend request.
We are still testing this out and it may very well be the case that private Snapchat stories are not sendable but that does not seem to be the case at the present time. This is going to be all kinds of drama moving forward if it is not changed.