Their biggest clients are hospitals and insurers. There are people called "frequent flyers" who come to the emergency room frequently and while they might only be 2% of clients they account for a huge share of costs. It's actually cheaper to hire social workers to provide these people with the things they actually need (i.e. treating the causes) instead of the symptoms.
Here's an example. Guy is low income. Cannot afford food & insulin for diabetes. So he chooses to not buy insulin and the food he does buy is high in sugar (think cheap whitebread). Goes into diabetic shock and gets sent to the emergency room. Instead it's much cheaper for everyone involved if a social worker finds out the problem, helps him research some foodbanks to cover his nutritional needs or gets him on a discount insulin program. It's not free, but it's much cheaper than trying to clean up a mess after the fact.