I'd like to download a full size profile photo of a long lost connection who has her profile set to private. Is there any way this can be done?

All I'm able to get is a cute little square crop with poor resolution when what I really want is to see just how low cut her top is.

Is there still a simple method of manipulating the URL? Can entire albums from private profiles be accessed through some exploit or internet based tool?

Any solution is greatly appreciated!