Concept for "when a mechanism exists which can be exploited, people will exploit it" I dimly recall a concept, I think defined by an economist, although I cannot remember the details or context.  I think an example--apocryphal or not--was welfare recipients who would have more children in order to qualify for more welfare.  I know that's a controversial example and am not claiming that the    phenomenon is real or wide-spread, but it's just to give a sense what the concept is that I'm searching for.  

In general the concept is something like: although you may create some sort of financial or political mechanism to serve one purpose, if people can use it for unintended personal gain then they will.  

I was wondering if anyone can name the concept for me so that I can research it further.  Also if anyone knows relevant literature from Economics or Social Science journals or academic publications, I'd appreciate it.
I think the broad principle you are looking for is: people respond to incentives. 

This is an important principle (some would say the most important in economics), with many implications and corollaries. But I think the particular implication you're looking for is unintended consequences.

So in your example, welfare was intended to alleviate poverty. However, because people respond to incentives, welfare has the unintended consequence that some people have more children.

(Other similar terms you may be thinking of: Cobra effect, perverse incentive.)