Does cash ever vanish into thin air?

Welfare: If you give a woman with kids X amount of money per month (forget the moral aspect) does it or does it not vanish? If it vanishes, where does it go? Or, does it get spent and eventually become someones wages, profits, savings, investment capital and finally local, state and federal taxes. (Answer this first.) Next: If that X amount of money wasn't used for 'welfare' would or would not the economy cycle down to a lower level as there would be less economic activity? Next: If all of this 'welfare' was cut off what in your 'opinion' would be effect on crime, child abandonment, hunger, evictions and other social problems. Would these problems be more costly, less costly or a wash if the entire concept of welfare payments be abandoned. Wow..what a mouthful! Try to be logical...not rants, or if you must rant make it interesting!