While this is old news, it is still interesting. (I will try to find more up-to-date stats later.)

The upper graph shows the persentage of people in each prefecture who received welfare benefits (生活保護, seikatsu hogo) in 2010. Starting from the left, the rate for the entire nation (全国) is 15.2%. Next is Hokkaidô (北海道) at a whopping 29%. Aomori, 20.8%. 19.5% of the residents of Tōkyō (東京) are on welfare; 15.3% in Kanagawa (神奈川). Ōsaka (大阪) has the largest number of welfare recipients at an unbelievable rate of 32%, meaning some 2.8 million people in the prefecture are receiving benefits. Kōchi (高知) on the island of Shikoku has a rate of 26%. In the prefecture of Fukuoka, where I live, 24.1% of the population is getting government aid, the fourth highest in the nation. Interestingly, in neighboring Saga prefecture (佐賀) the rate is only 8.7%.

The red line indicates what the rate was in 1997. In every single prefecture the rate went up, in many cases doubling.

2010 was not a bumper year in Japan. Thanks the what the Japanese call "The Lehman Shock" (and I call "The Panic of 2007-2008"), the official unemployment rate was at its highest level since the 2002 recession following the 9/11 terrorist attacks. It has since come down and now hovers between 3.5% and 4%, or at about the same level that was seen in 1997 when the Asian financial crisis threatened a global economic meltdown. (So many economic crisises are bad for the heart.) I would think that the percentage of those who are receiving welfare benefits today has also come down. (I'll have to look into that.)

One thing that struck me, actually several things did, but one thing that impressed me is how larger, vibrant cities like Fukuoka had such high welfare rates, while places like Saga which, I'm sorry to say, don't have a whole hell of a lot going for them—the same could be said of Hokuriku (Toyama 富山, Ishikawa 石川, etc.)—have such low rates. My theory for this is that the younger stratum of the population has left for bigger cities to look for work, lowering the welfare rates of their home towns, but raising them in the cities. (Visit Saga city on a Sunday afternoon and I challenge you to try to find a person in his or her 20s. They just aren't there.)

The second graph shows unemployment rates on the X axis and welfare rates on the Y axis. As one might suspect, there is a positive correlation between the two: the higher the unemployment rate, chances are the welfare rate will also be high. Fukuoka (福岡), again, had the fourth highest rates in the country in 2010. 

Here is information from 2018: