BSR lenders do not like to sell properties directly because of liability issues. A sale is a sale is a sale. So they usually broker out the sale. Many REO properties are on the MLS. Many were on the MLS and didn’t get sold then they were pulled off. Even all of the private auctions like REDC are brokers that represent the lenders on the selling side.
Obviously you can lookup the status of a home at sdlookup. If it is owned by a lender then it becomes REO eventually if it is not already. Someone posted a thread awhile ago with the names of several lenders. You can go to their websites and they have REO listings. The listing usually has the name of the listing agent.
There is usually a lag time from the lender taking ownership of a property to the property becoming an REO and being listed with a local broker. Sometimes it is quick and sometimes it is a bit longer, a few weeks.