I'm as confused as Randy with your question. I see at least three scenarios from your question -
1) A person lost their house and now wants to buy another for less money - If that's the case, the person who lost their house will likely not qualify for any loan for about 5 years. Foreclosure is a "Credit-Killer" and lenders just won't lend to people who didn't pay their prior mortgage. This person could purchase the house for cash but I think the prior lender who foreclosed on the property might have a method to go after them for the deficiency on the prior loan if all this cash re-appears. Also, they cannot re-purchase their prior (foreclosed) home, it must be an arm's length transaction - in other words not a relative.
2) A buyer is looking to purchase a property that was previously foreclosed at a much higher price than it is currently worth. In this situation the buyer must qualify with a lender to purchase the property unless they are paying 100% cash. It has nothing to do with the former owner.
3) Auction property - County / Lender Forecloure Auctions properties are to be paid for by Cashiers Check or using a Bank guaranteed Letter of Credit. Properties sold by Auction Companies such as REDC can be financed at the Auction after payment of 3% of the purcahse price is provided in certified funds at the auction. They have lenders on-site to close loans right there.
I hoep this covers your question - I'm just not sure !
Broker & Realtor
Orange County, CA