S'dom
Ten righteous people are not found and the cities are destroyed, but Lot and his family are spared. (We don't know, because they aren't the POV characters in the story, if anybody else was spared from either city.) Mind, we're dealing with a pretty loose definition of "righteous" (more on that in a bit), but nonetheless God does not destroy the righteous alongside the wicked, even if there are not enough righteous to provide a safety net for the whole area. Read this way it seems clear that the judge of all does do justice (as Avraham challenged); sparing the cities entirely might be closer to mercy than strict justice.
I can't say anything about Lot's wife and daughters (about whom we learn almost nothing), but Lot seems to have some problems with righteous behavior. Perhaps it is the corrupting influence of the city he chose to live in; surely he had the opportunity to learn better while in Avraham's company, but he didn't learn enough to stay out of bad neighborhoods. Despite that he starts out well enough, escorting the visitors to his house and offering them food and shelter (though one person in our study group noted that he, unlike Avraham, was ready to push them out the next morning). When the mob arrives at his house he steps outside and closes the door behind him to protect those inside. So far, so good, but we all know what happens next -- he protect the visitors at the expense of his own family. Bzzt. A truly righteous person takes on risk himself rather than using others as a shield.
And yet, despite the reprehensible crime he committed against his daughters, Lot was allowed to escape. The things he got right were enough for the divine judge to allow him to survive this destruction, apparently. The world is not so black and white as we would sometimes like it to be.
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http://en.wikipedia.org/wiki/Islamic_view_of_Lot
Interesting alternate perspective.
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That Wikipedia page says that both the Quran and the Hebrew Bible say Lot was sent by God to turn those cities from their evil ways, but I don't actually see that in our text. So read that with a grain of salt.
It's interesting that both Islam and Christianity (as I understand it) consider S'dom's sin to be homosexuality, while the Jewish sources I'm familiar with (commentaries and midrash) consider it to be the violence with which they treated others. The problem with what the mob wanted to do to the visitors isn't that it's male-male sex; the problem is that it's rape. I wonder how that difference in interpretation came about.
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The Christian view of Homosexuality, as I understand it, was actually shaped less by Jewish thought than by Roman thought. Male-Male sex was always a very controversial topic among the Romans, with the idea being "it is better to give than to receive", but even that had a stigma. I believe Rome adopted (took over, really) Christianity at a time when this was a hot topic. I am not sure what the Early Christians believed about it.