If I have an IG A and B list, where A is at 1 hull remaining (no shields) and B has all his hull but no shields, what happens if IG-B kills a Z-95 with dead man's switch, that in turn kills IG-A.

Does B get to recover a shield or not?

Yes. Peer the latest faq timing chart all 'after attacking/defending' abilities resolve before anything is removed, so b would regen the shield then the z is removed then it deals the damage, killing a.