Further to Michael's recent question and since I couldn't quickly find information on rejecting migrations from SO^H^H other sites...
How do you reject a migration and what happens when you do it?
A question that is migrated to another site is rejected by that site if:
To reject a question that's been migrated here, you should vote to close for one of the reasons listed above.
When a question is rejected:
I can't find a definitive reference, but there are a few mentions of rejected migrations being deleted on the site they had been migrated to. (After 30 days?)