And their goal?
Their goal was to find those people, keep track of them, and make sure they continue to go about their daily lives as usual with apparently no quarantine.
If that's the plan "detectives" were using in Liberia and S. Leone, then no wonder the disease grew out of control in those countries.
No, the disease spread partly because there were not enough "disease detectives" (aka epidemiologists) on the ground to conduct the contact tracing and monitoring that is necessary whenever there is a disease outbreak. There also are not enough medical facilities to take care of the sick, leading to family members becoming ill when they take care of their loved ones who have Ebola.
One of the major reasons we have the luxury to not worry about dying of some infectious disease is through the work of epidemiologists who figure out how and why a specific disease outbreak occurred, and how to contain it. The CDC has been doing this job behind the scenes for decades, and no one ever notices because, well, the CDC is very competent at this job. I should point out that the CDC does not do this alone; it works with local and state health officials to contain outbreaks.