Hardtimes:
Sorry about your misfortunes. You can always make a counter-offer to the bank and negotiate from there just do not wait too long to complete the transaction because at some point you will be court ordered to vacate and come out with nothing. As far as the date to vacate, once you agree to the money, you will need to move ASAP. The longer time period you request the less reason to pay you more. It is costing the financial institution money also and that time vs. money aspect comes into play pretty quickly.
As far as selling appliances, you are really not supposed to sell fixtures but I have seen it done.
Good luck to you.

Well, don't sell anything. If the property has been sold at auction, then it is no longer yours and you could be arrested.

Remember, anything and everything is negotiable. Allow them to make their offer and ask a reasonable amount higher. Plead your case and be honest. Tell them that the amount that they are offering is not enough to get you into an apartment. What do you have to lose. The only lower bidder is what ever it costs to evict someone in your area. If an eviction is $1000.00 and 2 months, then I imagine you can get 1000 for the key if you leave timely and cleanly.

Good luck.