Having failed to find someone that could reverse lookup the phone number, I decided to dispatch the number around to trusted people to see if anyone could come up with an entry in their own address books, some of which are fairly large.
So far no one has tracked that number down, but I'm still waiting for most of the results. However, it only took two hours before I found someone that had seen that number before: he has been receiving the same kind of message for a week, from the exact same number, except only fewer because he can't answer.
This is excellent news because he happens not to be part of my close friends circle, so that the number of people that we both know is rather small. We've merged our clues and have a list of approximatively three persons, two of which are rather unlikely. I've also played Chinese Portrait ("if you were a city/fruit/animal/book/etc, which one would you be?") with the mystery SMSer and what I got back does match suspect number one.
Of course, this is not sufficient to be certain and attempt to face her to clear things up. But it's enough to plan a small trap to check if we're right.
I must say that I'm still amazed how much you can learn from less than 50 messages, all of which must be smaller than 1025 chars, often much smaller. Of course, this is in the case of someone playing that kind of trick and with the premise that someone doing that always wants, one way or another, to be caught.
If it turns out to be who I think it is, I really don't know what to do though. If it's her it's not a joke, and she definitely has a problem of some sort. She's a nice but slightly lost girl that I only know distantly. If you have any experience in talking to people that have that kind of "problem" (quoting it here because it doesn't have to be a really important problem, maybe just sudden loneliness in a foreign large city and failing to deal with it) I'd be glad to hear about it.