Is there an average percent that banks will take on a foreclosed home?
No, there is not necessarily an "average percent" that banks will take on a foreclosed home.
When a bank forecloses on a home, the home is auctioned to satisfy the amount owed. Typically, a bank will make a bid in the amount of its lien. If no one else bids a higher amount, the bank becomes the owner of the home and the home becomes part of the bank's inventory of Real Estate Owned (REO). Once the bank owns the home, it hires one or more real estate brokers to give an opinion of the value of the home. These are called Broker Price Opinions or BPO's. Ultimately, the bank sets a selling price and hires a broker to list the house for sale.
Once the house gets listed and is on the market, the bank has to monitor developments, much like an ordinary home seller, and - depending on market conditions - adjust its price in accordance with them. Ultimately, the amount the property sells for, expressed as a percentage of the original asking price, will depend on those market conditions. In market conditions such as those we are seeing today, a lender may be willing to sell a property at a significant discount to its asking price in order to eliminate ongoing carrying costs. On the other hand, in "hot markets" such as we saw earlier in the decade, a lender could reasonably expect to get full price for its properties -- sometimes even more!
If I were shopping for a new house and liked one that happened to be bank-owned, I would probably work with a buyer's agent and try to come up with an offer that took both my level of interest and current market conditions into account, just as I would with any other home. On the other hand, if I were "bottom-fishing," I'd just make offer after low-ball offer until someone bit and, in the course of doing so, I'd end up learning a great deal about what works and what doesn't.
Best of luck!