Police said Monday a woman in her 30s is believed to have killed her preschool-aged son and herself over financial difficulties, showing that there are still blind spots in Korea’s welfare system.

The 37-year-old woman and her four-year-old son were found dead Sunday in a suspected murder-suicide at an apartment complex in Dongducheon, Gyeonggi Province, according to local police. The deceased woman, who lived in a studio apartment near the site, left her home around 6:00 p.m. with her son to go to the complex.

After investigating the scene, authorities found a tax bill with the words “I’m sorry” written on it.

Officials said the woman did not have a consistent source of income and that she also suffered from depression.

The untimely deaths are only the most recent involving those in financial straits.

Last week, a 61-year-old woman surnamed Park and her two daughters in their 30s were found dead in their residence in Songpa-gu, southern Seoul, with the traces of a burnt briquette, leading authorities to suspect suicide.

The three had left an envelope containing 700,000 won ($654) and a note saying, “I’m sorry, this is for our last rent and bills. I am deeply sorry.”

They had been living off the small salary Park made from her job at a local restaurant, but recent injuries kept her from working.

The family reportedly was unable to collect benefits because it did not fall within the parameters set up for vulnerable social groups. Park’s daughter reportedly suffered from diabetes and high blood pressure, but she was not handicapped and was not able to receive related benefits.

The Ministry of Health and Welfare on Monday announced it will conduct a nationwide research project throughout March, looking for those who fall between the cracks in the existing welfare system.

Working with provincial governments, the ministry will look into low income families, households that recently were denied welfare payments, and others who had been overlooked.

The government also said it will step up promotion of its social security system, since potential beneficiaries sometimes fail to receive funds due to a lack of knowledge.

“The ministry needs to revamp the system so it can find more people that need help,” said Welfare Minister Moon Hyung-pyo.

According to 2013 data by Statistics Korea, the country’s poverty rate is the sixth highest among all members of the Organization for Economic Cooperation and Development. The data showed that 16.5 percent of the population was in poverty, well over the 11.3 percent OECD average in 2012.

Other data by the Bank of Korea showed that the nation’s top 10 percent in the income bracket made 10.5 times more money than the bottom 10 percent. Only eight of the 34 members of the OECD had larger income gaps.

By Yoon Min-sik (minsikyoon@heraldcrop.com)