Faculty advisor is leaving, any way to turn this into a good thing?
In my opinion your friend should talk to the director of studies or whoever is in charge of the PhD program. They should explain that their situation is far from ideal and ask for advice. The objectives of such a meeting would be to:


Appear on the institution radar as somebody who may have face difficulties due to these circumstances. This can help the institution anticipate problems if they can, and could make them more responsive in case of more serious problems at a later stage.
Take any advice that can be offered: this might include suggestions to work with a particular professor or any other kind of help.
If they already have an idea of somebody they would like to work with, make a case for it: the institution might encourage the academic to take them on.
Gauge the level of attention/care given to their problem: for example if it turns out to be difficult to even talk to the person in charge, it says something about how much the institution cares about their students. 


In general it's a sign that your friend should not count too much on supervision in this institution. Maybe they can turn their attention and efforts towards collaborations with external researchers related to their topic. Depending on the institution response, maybe the positive perspective would be to embrace being autonomous and having more freedom to work with people they like.