Yes, throwing good money after bad is not a wise business decision.
However, with a $500-1,500 net loss each month that can be decreased with budgeting and one or two of the parents getting off of their butts and working another job, it would be better to work to pay off the reset. This is a fair price to pay for not going undergoing the trauma of foreclosure, especially for a family.
Again, this advice is for someone you know. And, no, it will not work for everyone. For example, if they are making $40,000 a year with a $780,000 mortgage, $40,000 in credit cards, and two new SUVs in the drive way, they should walk.