All the offers for foreclosures will be approved by the lenders. Most of the time they tried to get the properties sold as much as the current mortgage owed by the owners. The process will be long and complicated. If you have patience enough then you might get the good deal but there will be a lot of bumping during the transaction. You need to work with an experienced agent who knows how to handle the foreclosure transaction properly from a to z. Good luck.
If a property was sold for $400,000 at the peak of the market, and you get an offer accepted for $200,000, you are getting a 50% discount from the peak value. It does not matter the house is currently listed for $210,000 or for $ 199,000. - The current list price is not closely correlated to either its current market value or it's historic peak value. The only issue should be "are you getting the house for the lowest price you can get it or a similar house for?"
Nobody today will buy a house for its top value. Though many will sell you a house for half off the old price, no one will sell a house for half of its current value.