I'd rather there wasn't any official policy on this, and it was just solved informally among the concerned parties.
Either Alice can abstain from replying to Bob (answering in sister comments instead, if she really needs to), or Alice can reply to Bob at the risk of looking like a douche. It doesn't seem like a huge sacrifice for either party, and not one worth escalating over.
A more general policy that would be worth having is that if some users start creating too much drama and bickering between themselves, the moderators should feel free to start nuking posts.
In light of recent (and potential) events, I wanted to start a discussion here about a certain method of handling conflicts on this site's discussion threads, and hopefully form a consensus on when to use the measure described in the title. Even if the discussion has no impact on site policy ("executive veto"), I hope administrators will at least clarify when such a measure will be used, and for what reason.
I also don't want to taint or "anchor" the discussion by offering hypothetical situations or arguments for one position or another. Rather, I simply want to ask: Under what conditions should a specific poster, "Alice" be prohibited from replying directly to the arguments in a post/comment made by another poster, "Bob"? (Note: this is referring specifically to replies to ideas and arguments Bob has advanced, not general comments about Bob the person, which should probably go under much closer scrutiny because of the risk of incivility.)
Please offer your ideas and thoughts here on when this measure should be used.