What was the name given to the network of people dedicated to escaped slaves get to free territory?

The correct answer is the Underground Road! 
The Underground Road was a network of safe houses and secret routes in 19th century that the slaves could use to escape to the north or to Canada. People helping the slaves were both black and white and both free and slaves were helping too!

Underground Railroad

Provide more information so i can answer your question; )

Bbecause the jim crow laws were made to make voting difficult for african americans