The answer is: living arrangement with/without violent partner
Dependent variable is the type of variable which values depended on its interaction with independent variable.
To put it simply, dependent variable is something that you measure (or try to influence) during an experiment.
From the case above, the research tried different method of treatments and see which one would influence the subject the most and decide to leave their violent partner. From this alone we can say that the women's living arrangement is something that the researcher want to measure.