That's not accurate.
Group 1 had no wealth to transfer to the bank. The reason they are walking away from their mortgage is because they were underwater. If they had wealth in the property, they would sell it, pay off the loan and pocket their equity.
Here is the timeline.
Lender loans Group 1 person $500K
Group 1 person buys house for $500K (They have no wealth right now. They own an asset worth 500K and have a liability worth $500K)
Broker gets a fee from Lender. There is clear evidence that brokers got more fees for riskier loans (points etc.)
Lender securitizes and resells loan on the market. Buyers are largely institutional investors (i.e., my 401(k) and yours) and Freddie and Fannie (the taxpayer, at least after they were bailed out).
Lender makes big profits.
Executives at Lender take huge bonuses.
Rating agencies rate stinky bonds AAA. Get paid.
Group 1 person either makes interest only payments or mostly interest payments for a couple of years (basically renting money)
Market crashes and house value falls to $350K.
Group 1 person walks away with ruined credit history and hands over keys to lender.
Institutional investor, Freddie, Fannie, taxpayer, and MAYBE original lender in the rare case loan was kepttakes $200K loss after selling costs. On a national scale this was the 100s of billions of dollars in mortgage write-offs that have been recorded.
Taxpayers and shareholders of Lenders (again, my 401(k) and yours) absorbs most of the loss. Brokers keep their fees. Lenders keep their fees. Lawyers and ratings agencies who packaged bonds keep their fees. Executives of all of the above keep their yachts.
Now the lender might have changed as the debt instrument was sold, but the person who owns the debt is the person who lost all of the wealth.