Moderators can migrate questions to any site in the SE network. This can be pretty useful, but at the same time this means that we occasionally migrate to site we don't have much experience with.
SE encourages moderators to simply migrate questions that seem to be of sufficient quality and on-topic on another site instead of asking the target site mods. In most cases this is simply more efficient, especially considering the different timezones moderators can be active. But this way also means that we'll inevitably get it wrong at some point. That is no big deal, closing the question on the target site rejects the migration.
But what we don't really want to do is making the same mistake twice, learning from the rejected migration should help to avoid sending the same kind of question again. The problem is that a rejected migration is essentially silent, we likely never notice it.
What I'd like is a notification in my inbox if a migration I performed is rejected. This happens rarely enough that it shouldn't be noisy, and it would be pretty useful to understand the scope of sites I migrate to better and avoid repeating my mistakes.
Sometimes a migration is also not performed because the post is off-topic, but because the asking user requests it. In such cases I'd also reopen the source post if the migration is rejected.
I don't know the volume of migrations by mods on SO, but this might be something that should only be enabled on non-SO sites.
