> I think you are saying that in the US when you sell your house for less than the value of the loan, the banks takes the loss instead of you
This is generally the case with a voluntary sale at less than the loan value, but those are generally only possible with the consent of the lender (who has a claim on the property which must be extinguished for you to sell it.)
It is also sometimes the case in the event that the lender forecloses on the property for non-payment, and the foreclosure sale produces less than the amount owed on the loan -- but this differs between different states.