By the agent representing the owner of the property. If a home is on the market, but about to go into foreclosure, but hasn't yet done so, it can be listed on Trulia.com by the agent representing the current homeowner. Same is true even if the lending institution owns the property later. If they utilize an agent to market and sell the property, that agent can list the home on Trulia.com
Once a homeowner is 60-90 days behind on their mortgage, the lender files a NOD (Notice of Default) with the courts. Once the NOD is filed, it's public information and anyone can get the information. The websites that get the information ask you to pay a fee, but you can get the information yourself.