The most successful rebrands are continuous - the Kardashians. Madonna - because you keep the audience with you the whole time.
A second is the amnesia strategy - wherein you pretend "not to know" that brand you once were. Ronald Reagan the President not Reagan the actor, same with Schwarzenegger. Works of you can pull equity from the prior brand, e.g. polished or tough image.
A third rebrand strategy is the facelift - JC Penney - works if you stick with it and make it convincing. Difficult to execute though because it implies "aging brand" and a recognition that you dropped the ball for awhile.
A fourth is the apology - Domino's Pizza - where you simply vow to improve the existing brand. I like this approach though some disagree.
Yet a fifth is the drop-out-of-sight approach - Molly Ringwald 80's movie princess - you go away and come back as an icon for another era, e.g. a mom on ABC Family. Again related - mass entertainment - but a different niche.
* All opinions my own.