I'm assuming he had nothing of value when being released from prison (I guess all his possessions would be taken from him).
He stays at June's place, paying $700 a month . I'm assuming that he, as everyone else, has other expenses in his life that must be covered.
In (3.4) Peter says to Neal:
That's why we pay you the big bucks....if we paid you...
Ok, so it's pretty clear that Neal can get a lot of money by selling items he has hidden away somewhere. He could for instance (minor spoiler from 2.14):
sell the ring hidden in the statute in Madison Square Park worth $2.5 million. (2.14)
My question is: How does Neal make money... Or rather, how does Peter and the FBI think Neal makes money? Obviously they can't rely on him selling stolen goods.