It's most common to inform an investigative role if the target of its action has changed (e.g. via giving the name of the targeted player in the investigation results). It would be possible to design a Mirror variant which keeps the change of target hidden instead.
The Mirror has some similarities to the Bomb; both roles are capable of killing players who attempt to kill them overnight. The main difference is that the Bomb also dies in the process.
The Nexus is another similar role; both roles are self-deflective, but the Nexus targets randomly rather than deterministically.
Although the role is rarely seen (likely due to being too powerful), and thus variants are even more rarely seen, it would be possible to create an X-Shot Mirror (likely the Activated variant) in order to tone down its power somewhat.
Use and Power
A Mirror role is intensely powerful at protecting itself; not only is it impossible to do anything directly to a Mirror at night, it will even kill people who try to kill you (which can only backfire if you belong to an uninformed faction like the Town, and there's a Vigilante in the game, although this is of course entirely possible). It can also be confirmed by almost any investigative role (sometimes even if the change of target is kept hidden, e.g. a Tracker will see fairly distinctive results in a mirror). This means that they only really fear the elimination, which still works normally on a Mirror.
It is typically not beneficial to claim Mirror, because the role becomes somewhat less powerful once people know about it, and its powers are far more likely to hurt your enemies than they are to hurt your own faction.