Well, 20 emu is quite a lot, not an easy species to place, and perhaps still today with some commercial value? I have worked somewhere in the past where our emu chicks went to ostrich farms, 'to become breeding stock'.
I don't think you're likely to hear of most species leaving. I do know 3 ground hornbills went to Drusillas, I think they are housed where the snowy owls were.
The fact that Cricket supposedly still has fallow deer should indicate that they might not be so keen to euthanase healthy animals....these would almost certainly have been culled rather than placed elsewhere IMO.
Although the current management are not connected, I'm sure there is distant memory of the controversy created when Sahib, a healthy bull elephant, was euthanased at Cricket with a rifle after not mixing well with the females and, I imagine, impossible to place elsewhere being hand-reared and not a well-socialised bull.