No. It is based on the total amount of money the lender needs to recoup their loss from the borrower. Actually it isn’t the total amount as much as it is the agreed or calculated amount the lender decides is sufficient to sell the property at the sheriff/ foreclosure auction.
Often you will see the lender buy-back the property. This is due to their minimum or starting bid not met. They will then take the property back into REO (Real Estate Owned) department and work with selected Realtors to liquidate it.
The dollar amount the lender considers to start the bid at a foreclosure auction is based on a percentage of the total amount owed to them from the borrower. Sometimes the lender will only need their principle dollar amount owed to them to agree to sell the property at auction. The tax amount only matters because they will stay with the property after the foreclosure. The new buyer will have to pay for them. I hope this helps.