Yes, it's a real word. It's the Konjunktiv II of brauchen, 1st or 3rd person plural, as you already know: http://www.duden.de/rechtschreibung/brauchen You use it as the Konjunktiv II of brauchen. :-) Sometimes the Konjunktiv forms look weird, so people use the auxiliary form instead (brauchen würden). But in this case, it's not so weird that nobody would use it anymore.