How do you get a good job without a college degree??
Claim unemployment, ballin off the state bro.
In this context, ballin used in the slang sense. From UrbanDictionary:
1.) To play basketball. 2.) Living in affluence/wealth.
The writer is using the word in the second sense, to mean living well. "Ballin off smth." refers to the source of the money that allows the speaker to be 'ballin'. In the particular context you've given, the speaker is using the term somewhat sardonically/sarcastically, as clearly no one living of unemployment benefits will be living in great affluence or wealth.
In my understanding, the term follows from the lifestyles of basketball players; to spend extravagantly at nightclubs or buy lavish cars is the epitome of 'ballin'. It reached the popular consciousness via Jim Jones.
NOTE: I'm being a little facetious in giving this such serious treatment. This phrase is about as far from standard English as could be and is totally inappropriate for any serious use if you're not a rapper.