People were paying toward a house. But if they missed a payment the deal was off. The Clintons kept all the payments *AND* owned the house. To be fair to the Ann Arbor bank, I'm not convinced that their Muslim banking program is as unethical as the Clintons' behavior at Whitewater.
You describe a Contract for deed sale. It is legal and at least in my part of KY quite common. It really preys upon people who can not get credit or don't qualify for bank loans. The owner/seller hope and pray the buyer defaults.