"We heard that she was unhappy."
Translation:Slyšeli jsme, že je nešťastná.
I am not a Czech expert neither, only native speaker.
"Slyšeli jsme, že byla nešťastná" - sentence testify only about the past, she was unhappy then, now she is happy or we don't know
"Slyšeli jsme, že je nešťastná" - imply continuation to the presence, that she is (probably) unhappy to this day
One of the Czech experts can give you a more authoritative answer, but I don't think that this is wrong. Here is the scenario I can imagine:
A says to B: You know, I'm really unhappy these days.
B says to C: A just told me that she's really unhappy.
C says to D: Guess what... I heard that A is really unhappy. Now's your chance!