If you'd like, you could have her family settle down in Ul'dah along with most other refugees. Ul'dah, however, is a brutal place for refugees and you can see lots of them are beyond poor, most without so much as medicine. It could be that her family had managed to bring some money/jewelry/etc with them (I imagine some refugees would have once been healthy and/or influential). If you like the idea of tragedy/having lost everything, her family could've eventually fallen into debt and lost everything they still had, and she could've used the last of the money to move to Gridania (I'm assuming the trip would be easier than a trip to Limsa, which is much farther away and accessible by ship or airship only).
There are quite a few scenes/quests with refugees being abused in Ul'dah, as well as at least one scene that comes to mind of debt collectors threatening someone, so it's reasonable for her family to have met a less than savory end once they were no longer rich.
That would probably give her a grudge against the way things are run in Ul'dah, though, which may not be what you're looking for.
There are quite a few scenes/quests with refugees being abused in Ul'dah, as well as at least one scene that comes to mind of debt collectors threatening someone, so it's reasonable for her family to have met a less than savory end once they were no longer rich.
That would probably give her a grudge against the way things are run in Ul'dah, though, which may not be what you're looking for.
