Between and Rock and a Hard Place - Impossible Short Sale in Grand Rapids MI

Well, it's official.  After all the short sales I've encountered I never thought this one would be the impossible one.  The short sale lender won't even talk to me about the impossible situation they have put me in!

I've had this listing for a dear friend of mine for many months now.  We tried selling it high enough so they wouldn't have to do a short sale first, but that didn't work.  The neighborhood's values have plummeted and the increased crime in the area has not helped.  We had to keep lowering the price until finally we got down to $32,500 and FINALLY got a cash offer of $22,000.   We even tried to counter the buyer's offer directly before submitting it, but he wouldn't budge.  The house is in pretty deteriorated condition.

Today we got an answer from the lender, yay!  They are countering at $38,000, boo!  *head desk*   They won't even listen to me about all the knowledge I have about this house and the neighborhood and the listing history and how impossible that is!!  They just rely on one stupid BPO.   I asked them to do another BPO, once again, ignored.  I asked them what our options are even if the seller has to sign a note (I know they would try to be as cooperative as they can, they just want to get this behind them) but they say any note would be for the deficiency not to make up the difference between the value and the offer.

So I am trying hard to help my friend avoid a foreclosure on this house that has plummeted in value since they bought it and then moved away from it a few years later due to a job she received that included housing.  They tried renting it out for a few years but renters just kept trashing the place forcing them to sink all kinds of money into that they can't afford anymore.  They just need to get this behind them, will they be forced into a foreclosure just to get rid of the house?? 

I thought banks preferred short sales to all the costs of foreclosure and holding real estate, am I wrong?

There is no way we will get an offer at the $38,000 price they are forcing me to re-list it at.   So they have forced me and my sellers into a spot between a rock and hard place with no where to go.  Any suggestions???