There is no easy answer to this question. It seems like she is a really important friend to you and you do not want to hurt her feeling! I can see where you are coming from, but by not doing anything you may be hurting her and your friendship more.
You have already identified two possible ways of handling it: talking to her about it or talking to her parents about it. Unfortunately, you are not very happy or at ease with either of them. However in order to address the problem, you may need to do one of these things. It would be almost impossible to address this issue anonymously. Sometimes in life we have to make decisions that we are not really comfortable doing, but we know it is for the best. You are concerned about a friend who may have a serious problem and this cannot go on forever. Stealing is not right and may get her into real trouble.
Regardless of whether or not you talk to her or her parents about it, you need to try to do it in a non-threatening way. An example of the start of the conversation can be, "I am concerned about you (or your daughter or son) because I think you (he/she) may have a problem with taking other people's things." Be ready to give examples and listen to her (them) too. She may get mad and walk out or she may admit to it. Either way, you have addressed the problem and she knows you are on to her. This is a start. If she does admit to a problem, you may want to give her suggestions on how she can get help like from her parents, school nurse or guidance counselor. If you talk to her/him about it and do not feel comfortable with the response to the situation, you may want to talk to her parents or your parents about it.
A couple things to remember is that:
Lastly, you mentioned that you think this is common and may be a problem with many teens and their friends. TeenHealthFX and other most specialists believe that stealing is not the norm for most teens. In fact, most teens believe it is wrong and do not participate in this activity.