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 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!