How long could they feasibly survive off of 500,000 JPY? I have no idea what the cost of living is in Japan.
For simplicity and the fact that Rinko said that her family was poor, I will calculate the average monthly cost for Rinko assuming the minimum cost for rent, utilities, and groceries.
Rent for a two-bedroom is between 12,000-60,000 yen so I would assume her mother did not rent the cheapest apartment I would assume rent to be around 15,000 yen per month with the utilities costing around 10,617 yen (gas = 2,920 yen, water = 2,245 yen, and electric = 5,452 yen) and her groceries to be around 21,667 yen for two people (Riko and Haruno) or 7,216 yen for instant ramen (100 yen each) and barley tea (180 tea bags for 1,133 yen) for two people (Riko and Haruno).
Given that the average monthly salary is around 180,000 yen which would mean that 500,000 yen would last almost three months for a family that has someone working and the monthly expenditure for basic living expenses is around 47,284 yen per month for basic living expenses which would extend the expected three months to around eleven months if every yen is watched.