Using the institution of Mutah, it is very possible for a woman to gain a living by doing Mutah with one man and then immediately marrying another man, and so on and so forth. To the unbiased observor, this woman would be nothing more than a prostitute.
The following question was asked on Al-Islam.org, the authoratative Shia website. The scholar passed the following Fatwa. No comments necessary, as it speaks for itself.
Making a living from Mut’a Marriage
Is it haram for a woman to make a living at mutah by marrying a man for a short period, receiving a mahr, then observing iddah and marrying another man for a short period and so on so that she is married to say half a dozen men in the year? If it is haram what makes it haram if she is observing the rules for mutah properly? And if it is not haram, does she deserve to be condemned as immoral (or do the men who marry her deserve that)?
It is not haram for her to make a living in this way if she follows the rules of Sharia properly. Nor does she deserve to be condemned. This also applies to the men who marry her.