What you would do is have an agreement in place with a lender for a bridge loan and have your current home as a cross collateralization.

., the property) against claims which would reduce the value of their collateral.

The Collateral must cash enough to support whatever LTV you are attempting to acquire it.  

Right now we are not selling anything or cashing out that equity - if anything I would look to acquire a property and find a HML that would cross collateralize one of my other assets so I don’t have to sell it but use it as collateral.

Tell them they can use that as collateral.  

Put up other collateral or increase your offer.

Balance sheet and depository relationships (some banks requiring upwards 10% of loan amount) are being prioritized over merits of the deal/collateral.

You’re giving them negative collateral. 

The whole reason FHA developed a short sale method is to reduce the loan balance down to reality, down to what the home is worth, down to the value of the collateral at the bank accepted. if they had the cash, they wouldn’t be behind on their monthly payments.You're right I overlooked that part.

Since lenders will not lend cross-border, you'll have to provide US collateral, like taking a HELOC if the collateral is real estate, or you'll have to use love money or pay cash.But maybe it's not that a bad thing if your land has increased in value in case you'd want to sell it you can't get the funding.