Accepted by whom? The owner? If the answer is yes, then the answer to your question is also yes. The owner may accept an offer, but the bank has to approve the offer also since they are the ones agreeing to take a loss on the sale. Typically the bank orders an appraisal or a Broker Price Opinion and then negotiates the original offer from there. Sounds like this is what happened in your case. Your options now are the same as with any other counter offer, accept it, reject it, or counter with a counter offer of your own.