One thing Americans might fall into thinking is that they poor family in the movie is similar to welfare queens in US. Afaik, there isn't enough support for one to live as a welfare queen in S. Korea.
Another different factor is Jeonse. In S. Korean real estate rental market, monthly rent is rare. Most are rented out as Jeonse. With Jeonse, instead of paying monthly rent, a renter will make a lump-sum deposit on a rental space, at anywhere from 50% to 80% of the market value.
This allow a poor family to have relatively secure housing (although it would be undesirable) while having no money for other essentials.