One is complicit when one actively aids, encourages, and abets others' wrongdoing, not when one does nothing. But most recent papers invoking the concept nevertheless mistakenly claim that doing nothing = complicity.
My hypothesis about why this move is popular is that it's an attempt to transform a positive obligation into a negative one. There's generally a higher justificatory burden in arguing that people have a positive duty to do something (e.g., feed the poor) rather than a negative duty not to do something (e.g., refrain from exploiting the poor). By conflating doing nothing with complicity, theorists lower their argumentative burdens, because they can now cast the positive duty to help as a negative duty to avoid complicity.
It's bad work, though. It would better just to argue that we have positive duties to help. It's OK to do that, fellow theorists. People have some positive duties.