Can someone explain what determines the sale price of a foreclosed home?

Banks can be difficult to work with. A matter of fact only about 10% of short sales go through. That being said, there actually may have been some logic in your friends case.

Without knowing the details of your friends situation, I'll share a scenario.

Fact: A short sale has to be approved by all parties. If you friend has a 2nd loan holder that was different then the first, the 2nd has to agree and accept what little money the first is willing to give them for the short sale to go through. TO give you an idea how little the 2nd may receive, one bank offers $3000 to the 2nd if it amount is under $100,000 and $5000 if it is over $100,000. That's it! Sometimes the 2nd rejects the offer because they can get more money if the sell the debt to creditors ( Watch out , depending on the state and the type of loan they had, creditors have 4 years to collect any un-recovered debt.).

If the 2nd doesn't agree, then the 1st lender can't get the offer accepted and may just cut their losses and foreclose.

Banks have different criteria for how much they will sell a foreclosure for. If it's an arms length transaction it usually depends on the amount owed on the mortgage less their formula for acceptable loss. This includes several factors such as how long the mortgage was in effect. I've seen a few deals where I know it wasn't an arms length deal and in that case there is no way to make sense of it.