In modern Secure Multi-party Computation (SMPC) protocols (informally) the notion of Fairness and Guaranteed Output Delivery (GOD) is defined as follows:
Fairness: If the adversary gets the output of the protocol, every honest party should get the output as well.
GOD: Honest parties should always get the output independent of adversarial behavior.
As I understand the seminal paper of Cleve'86, it proves that bias-resistant two party coin tossing protocol is not possible in honest minority setting. In particular, Cleve86 shows that if the honest party decides to output when the adversary aborts, then there exists an adversarial strategy where the output will not be equivalent to the output of the ideal coin tossing protocol.
What bothers me is that several paper cites Cleve86 and state that it is not possible to have fair (modern notion of fairness) protocol in 2PC. I am not able to connect Cleve86 result to current notion of fairness we talk about it Secure MPC protocols. Specifically, Cleve86 do not say anything about whether the adversary (whenever it aborts) gets any information about the output of the protocol or not.
Consider a protocol where honest party do not produce an output whenever the adversary decides to abort. Is this protocol not fair (with modern notion of fairness)? In my understanding, Cleve86 result is not applicable to this scenario.