There are plenty of examples of magic outliving its creator; death does not undo all the magic you have ever done. Consider things like:
! <PERSON>'s protections on Hogwarts, <PERSON>'s father's and <PERSON>'s protective charms on number 12 Grimmauld Place, the magical properties of ancient magical artefacts and all the permanent sticking charms.
I think you have to have to view some magic as active and some as a permanent change of property. Your grip on somebody's body or mind might be something that might only last as long as your magical powers allow, while transfiguring indicates that fundamental change and would outlive you.
Accepting that gives you two ways to look at what <PERSON> did:
* An active, imperius-style mind control. She could instruct them to leave the country and use her not-insignificant willpower to suggest they are different people, all without tramping on their underlying minds. Her death would mean they they remembered but by that point their strategic value (eg targeting them to get to <PERSON>) would be gone. 194
They'd still be safe.
* A fundamental change of their minds to remove (or otherwise block) certain memories. It wouldn't reverse on her death, leaving them ignorant to her existence and demise. That said, obliviate was demonstrably dangerous and could irreversibly corrupt minds (<PERSON>).
Either keeps them safe. I disagree with the current high answer, I don't think <PERSON> would have had any use for them other than as a pressure point for <PERSON>.
The only mentions of memory modifications in the books are linked to the obliviate charm, so you would assume the second would be more true (especially if you infer a lasting blissful ignorance for her parents) but the danger of performing such a fundamental change on their minds might suggest it wasn't.
Ooo, with help from the Harry Potter Wikia page on Memory Charms, we can see that it wasn't obliviate:
!In Chapter 9 of Deathly Hallows, just prior to erasing <PERSON> and <PERSON>'s memories, <PERSON> says that she has never performed a Memory Charm before, despite having already altered her parents' memories.
There's a webchat with <PERSON> where she confirms this:
! They are two different charms. She has not wiped her parents’ memories (as she later does to <PERSON> and <PERSON>); she has bewitched them to make them believe that they are different people.
As far as I know, there are no uses of this charm in the books that we can use to determine its permanency though. 45