Other than during pre-foreclosure, there's only one time when you can negotiate, and that's when a property was up for auction but didn't sell, and instead became real estate owned, or REO.
The lender with an REO is motivated to negotiate with you. The company has no interest in owning the home and will gladly forego costs associated with maintaining the structure, property taxes and even fines if the property condition lapses.
For these reasons, a bank will negotiate with investors in order to recoup some of the loss and get rid of the responsibility of the home. A lender with an REO is likely to negotiate the price of the house itself as well as repairs.