What is the symbolism of Alice's scar in the play, Closer?

In the first scene of the play, reference is made to a scar on Alice's leg. There are several stories told about where the scar came from: Alice tells two of them, Larry hypothesizes the third. The actual truth of what happened is never explicitly defined, but nevertheless, the scar can be seen as a symbol of whatever inner scar Alice has that has made her run away from her identity.