While everyone accepted the OP's story at face value, there are a few questions:
1. re: student loans - if they were having financial problems, I thought they'd be able to defer the payments
2. re: variable rate mortgage - *I* have a variable rate mortgage. It was the only financing that our mortgage broker was able to secure for us that would allow us to close within 2 weeks of the day he was hired. My payments went *DOWN* this year because interest rates are so low. Thus far, there's been no need or reason to refinance to lock in an interest rate. The principal is so low that we really wouldn't save that much. I'm not familiar with every type of home financing, but it seems that a variable interest rate wouldn't be the reason for their foreclosure either.
3. If they have the insurance as you're describing, it's quite likely that they're coming out ahead with this arrangement. I've even thought of doing that, but my employer and my wife's employer don't pay enough for the buy out. Which is something I can't quite grasp the logic of - the difference between what my employer would pay me not to have insurance, and what they actually pay since I don't take the buy out is over $11,000. If they split the difference, I'd take the buy out in a heart beat.
However,
#4. They *gasp* was their dishes by hand?! OMG! With one of them home all day, how do they find the time? Oh, the humanity! They're like the Amish or something! Can't they afford a dishwasher? Can't they afford soap for the dishwasher? (on a side note, do *NOT* use dollar general's cheap brand of dishwasher soap - it sucks. 1/2 a bottle later & we're back to the good stuff.)