If we stop subsidizing their existence they'll eventually go away.
It all starts when they are young (whether they are perpetuating their parents situation or just trying to be dumb and lazy). If you drop out of high school your driver's license gets taken away until you decide to educate yourself (go back to HS, go to a GED program). No DL = no subsidies. Also, put time limits on these things, limit the number of months people can be on these subsidies. On top of that you should be require to prove that you are seeking an education (college, community college, technical school, etc.).
Then the government could issue grants to local charities (churches, food banks, shelters, etc.) to help out w/ the people who do not wish to become educated in the least. This would cost the government less and the local charities would be much more efficient with the money issued via grants than the government would. I would also suggest huge tax breaks for private companies who donate large sums to charities.
What about people with hardships? Well, lets just give them help for very short time frames to get them through their hardships. If what the gov provides isn't enough for them they can look to local charities.
It's amazing what people can do for people. For example, lots of charities actually care about the people and attempt to do something to remedy the cause of their situation, while the gov just gives them a check so as to perpetuate the situation. It's the old "teach a man to fish" thing.