How does a short sale house work in US ?

The bank agrees to stop selling the property, and you take the money from the sale as payment in full of the mortgage. Without a short sale if the house sells for less than you owe, the bank will probably not allow the sale, and if they do, you will pay the difference between the balance of the Mortgage and the amount of money from selling house brings.

Both parties agree

A short sale is not something that can only do. You have to make the Bank agrees. That is not easy.