a1) They could have said they would have given up their dream.
b1) They could have said they would give up their dream.
Which one is correct? Isn't it the so-called double conditional, which makes (a1) incorrect? I tried to make it a little bit easier and rewrote those sentences in the present tense, but still, it doesn't make any sense.
a2) They could say they would give up their dream.
b2) They could say they will give up their dream.
I feel like (a) is incorrect in both dimensions, whereas (b) acts like some sort of mixed conditional here. Am I wrong? Maybe all of these sentences are correct. If so, what's the difference?