How can Cleve's 1/r lower bound on the bias of coin-flipping protocols hold if parties can output random bits? I was reading Richard Cleve's 1984 paper on coin flipping protocols, and he says that in the case where parties may abort prematurely and the honest party is forced to output a bit, then the honest party can be forced to be biased by at least 1/r where r is the number of rounds.

Recently Moran, Naor, Segev showed that this bound is asympotically tight.

Although I roughly understand Cleve's proof, I don't understand the premise that the chosen bit that a party outputs when the other party aborts is deterministic. Since they are PPTs, and they are notified when the other party abort, can't the honest party just flip a random coin and output that?
In a multi-party protocol, if every honest party just outputs a random bit, it's likely they won't all output the same bit and the protocol would be incorrect.

With two parties, the corrupt party can still bias the output. Suppose the corrupt party aborts in the last round whenever the actual protocol output would be 1. If an abort occurs, the honest party outputs a random bit. Then we have two cases, which each occur with $1/2$ probability:


Abort, output random $b \leftarrow \{0,1\}$
No abort, output $b=0$


Clearly the probability of outputting 0 is $3/4$, so there is still bias.