That depends on who the lender is and what type of loan is on the house. Basically at this point all you can do is wait. The bank will review the sellers financials, income, hardships, etc. and decide if they qualify for a short sale. If they do, then depending on who the lender is and whether the debt is a government insured loan or not, they will do their own appraisal and either accept your offer or counteroffer for more money. Some banks take longer than others and some are more flexible than others. You just have to let it take its course.
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I would just add that you may want to confirm that someone is working on behalf of Seller (either Seller's agent, Seller's attorney or some other third party) to stay in communication with the Seller's lender to keep the file moving through the review process. If someone is not following up with the Seller's lender frequently, the file can linger and you may end up waiting around for a response longer than you would like.
Also, you may want to find out whether or not the Seller has a Fannie Mae loan. Fannie Mae has a process for contesting their appraised value. If their value comes back higher than your offer, you can appeal and try to get Fannie Mae to reconsider. You would have the opportunity to submit supporting documents, such as your own appraisal (that your lender conducted) and/or comps from your realtor.
Please note that this answer is not legal advice and is informational only. We are licensed to practice in PA & NJ only and suggest that you consult with an attorney in your jurisdiction.
Please note that this response in informational only and not intended as legal advice nor does it create an attorney-client relationship with you. We are licensed in PA & NJ only. You should consult a qualified attorney licensed in your state.