I can't find anything like that on the homepage, but I'm wondering whether Star Alliance has a program like this. So basically, that I would get some miles if I recommend an active friend to also join the program.
Star Alliance doesn't have a loyalty program.
The individual airlines within the alliance each have their own loyalty programs, and each program has it's own criteria/promotions/etc.
You would need to check with the individual program that you're a member of to see if they have any such promotions, but at least the few that I'm aware of do NOT have anything like you've described.