Are there any non-profits that have to do with the abolition of slavery in modern times?

Yes. One non-profit organization is called PEHT (The Project to End Human Trafficking).

The excerpt below speaks of the motivation for the beginning of this program.

"The initial goal of the founders was not to begin an organization, but simply to offer educational lectures about human trafficking. They quickly found that the need for information about slavery was great and they consulted with similar groups, such as Free the Slaves, to determine the best way to move forward with their work. Today, PEHT engages in anti-trafficking coalition building, educational outreach, direct service to victims, and collaboration with other national and international organizations in the global fight against human trafficking."

Follow the link below to find out more about what they do there-

source: http://www.endhumantrafficking.org/