Blood

After getting hit with a nasty curse during the Battle of the Department of Mysteries, Hermione Granger makes a decision that will forcibly alter the course of the war dramatically.

She asks Lupin to Obliviate her parents and send them to Australia.

The summer before her fifth year she and Harry learn from the goblins that the two of them could, in theory, preform a blood ritual and make her a Potter by blood, a sister.

After looking into it they discover that the ritual would wipe all memory of Hermione Granger from the minds of anybody who ever knew her and replace her with Hermione Potter, the slightly older sister of the chosen one.

Not only would it remove the memory of her past life from those who knew her, but it would also embed the memory of Hermione Potter into the minds of Harry's relatives.

The ritual would drastically alter Hermione's appearance and make her look the part of a Potter...

It would offer her safety in a new identity and he a family he's always wanted.

So they do it.

In secret, not even telling Dumbledore of their intentions.

Nobody questions when the time for sixth year rolls around when Harry Potter boards the train and Hermione Granger does not.

Blood is thicker than water after all.