An extremely useful resource answering your query is a study by LaDonna Pavetti
I quote "....
The welfare system is an extremely dynamic system. In an "average" year, about one-half of the AFDC caseload leaves the welfare rolls. The best available estimates indicate that between one-half and two-thirds of those who leave do so because they have found paid employment. A small percentage (less than 15 percent) leave for marriage and the remainder leave for a variety of other reasons. Those who leave are replaced by new applicants who have never received assistance before and by families who have received assistance previously and are returning to receive assistance again.
The majority of families who leave the welfare system do so after a relatively short period of time -- about half leave within a year; 70 percent within two years and almost 90 percent within five years. But many return almost as quickly as they left -- about 45 percent return within a year and 70 percent return by the end of five years......"
A complete resource is available on http://www.urban.org/publications/900288.html
I am sure the above shall help...