There are only 16 states that recognize common law marriage, only 10 of which still allows it today, the other 6 recognize it before a certain date for example Ohio only recognizes common law marriages created prior to oct 10th 1991.
Even in those 10 states that recognize common law marriage there is a specific set of circumstances that need to happen for you to be considered involved in a common law marriage, so it's not going to be a case of some guy living with a woman and being married without them actually knowing it.
For example "living together for 1 year, intend to get married and hold yourself out to be married and claim married on your income tax"
So you know for a woman to try what you say in order to get alimony payments without you being well aware that you are in a common law marriage is not going to happen. It's going to be more of an instance of damnit, i knew i shouldn't have claimed married on my taxes to get that tax break. Or crap, i shouldn't have proposed to my live in girl friend and then back out of it at the last minute.