Consider the Elizabeth Smart case. People never gave up searching for her, even outside of UT. Several months later, someone recognized her in CA & reported it to the police.
Posters will often state that LS cannot be alive, because she would have called her parents by now. ES apparently had had opportunities to contact her parents, but didn't. Sometimes people are manipulated to behave in a way that one would not expect.
LS being alive is not impossible, however improbable it may seem to some observers.
I keep thinking about the runaway bride case. Remember that? The woman who made up a story about being kidnapped and then stayed away for awhile? I know it's not at all likely, but the part of me that wants a happy ending keeps thinking...maybe she just passed out somewhere, and by the time she spent 14 hours sleeping it off, there was already a full-out search going on for her and she was too embarrassed/ashamed to come forward.