Rules FAQ pt 1
From RRG pg 18: A replacement effect is an effect (usually an interrupt) that replaces the resolution of a triggering condition with a different means of resolving that same triggering condition, but in such a manner that the triggering condition is still considered to occur. The word 'instead' is frequently indicative of such an effect. After all interrupts to the triggering condition have resolved and it is time to resolve the triggering condition itself, the replacement effect resolves instead.
Claim replacement effects are triggered during the C step of DUCK (after Determining the winner and gaining the Unopposed bonus but before Claim is applied). These effects do not resolve immediately, rather they modify the way claim will be applied after all interrupts are played. For example, with Mirri Maz Duur you choose a character, and set up an effect that will kill that character when claim resolves. But after you trigger Mirri, and before you resolve claim, your opponent might play his own interrupt to applying claim (like Vengeance of Elia) and set up a new effect that will modify the way in which claim will resolve. This new replacement effect will override the previous one. Once all players are done playing Interrupts to "when claim is applied", resolve the claim in accordance with the most recently played replacement effect.
Rules FAQ pt 2
Mirri's "attacking alone" triggering condition is checked when claim is applied. Any characters that were attacking with her but were removed before claim (step C in DUCK) are irrelevant. For example, you can attack with Mirri and The Hound, bounce the Hound in step D, and trigger Mirri in step C.