It should not be that hard to come up with $687 a month that they would end up losing their house. Certainly there are other expenses, but with the mortgage at the top of the list, everything else comes after.
In response to your particular situation, I know it is tough. I have been there. Out of work, unemployment compensation wholly inadequate. Bank sending notices. Creditors calling. Had to take a job on a temporary basis that paid a whole lot less than I had been making.
We got out of trouble by making major budget cuts.
-Food bill was down to $35.00 a week for family of three.
-Cut out every other non-essential expense.
-Dishwasher became a drying rack, Never turned on.
-Clothes line instead of clothes dryer.
-2 minute showers.
Electric bill went from $180 a month down to under $50 a month. Gas bill went from $65.00 to $11.00 a month.
To save on home supplies, we did things like use the plastic bags they give you for free when they pack your groceries in instead of buying plastic bags. Cut our waste down by buying things like concentrated OJ instead of the big gallons containers that took up a lot of room in the trash can. That eliminated the need for trash service. We just packed small bags of trash to public recepticles.
We actually found we could get by like that and have some money left over at the end of the month.
I hope you can make it out of your situation okay. Don't mean to sound uncaring. Just trying to point out that there are a lot of ways to save money.