This really depends on many factors, who the lender is, who the investor behind the lender is, how much lower?, how long has the home been on the market, were there other offers, does the Realtor have any substantial and relative market data to demonstrate why the offer should be accepted, and more...
The short answer is, most of the time the bank (lender) will want to renegotiate if the appraisal comes in lower than the offer price. The bank is typically not going to accept an offer that is substantially lower than the market or appraisal price. This is especially true if the seller or sellers Realtor/negotiator cannot demonstrate a strong case otherwise. The bank (lender) usually wants to see the home on the market for at least 90 days with realistic comps and an appraisal to substantiate the accepted offer price.
These are questions however that you should be discussing with your real estate professional. If you need additional information, please feel free to visit my site at www.ForeclosurePreventionResource.com for resources and information about foreclosure prevention and the difference between short sales and foreclosure. Or you can visit my personal site, www.TimDenboHomes.com
I hope this helps,
Tim Denbo, CDPE
Certified Distressed Property Expert
P.S. Free Foreclosure Prevention for Homeowners Seminar - September 30th, Hilton Pleasanton. Register online at www.ForeclosurePreventionResource.com