You need to have your Realtor do the comps on the home to determine if it is priced correctly or not. If the home is already very well priced (ie below market value )and you come in with a low bid, you will just insult them, unless they are truly desperate. if they aren't desperate and can afford to wait, they will either not answer you back at all (which is an answer) or they will come back close to a full price offer (some if truly insulted will come back over their list price). As Brian noted, if you really insult them, then they may not want to deal with you at all. I would put together a letter about your family, describing yourselves and why their house is the perfect house for you, to put with your offer. If someone truly loves their home, they sometimes accept a lower offer because of emotions. BUT, if they need all the money out of this one to pay off their mortgage or if they are already paying 2 mortgages, they will not be swayed by emotions, but by their pocketbook.
Each market area is different. In St Louis, different neighborhoods are different. I've got areas where the prices NEVER dropped and continued to climb. Other areas where prices stabilized over a year ago and are moving back up. A good home, that is correctly priced for it's condition, location and amenities is still selling in less than a week in my area. Ask your realtor to do the comps and let you know what the absorption rate is - ie how many homes typically sell in a year in that area, then how many are now on the market (ie how many months worth of inventory are on the market). That puts reality in the picture. If 2 homes sell in that area in a year and there are 6 homes on the market, you have a 3 year supply on hand. when faced with those facts, a home has to be better than all the others in order to win the prize (ie your winning contract)