"Encourages" is an antonym for the phrase "puts a stop to." When someone puts a stop to something, they halt or prevent it from continuing. However, when someone encourages something, they promote or support it, essentially helping it to continue or move forward. Other antonyms for "puts a stop to" include "allows," "permits," "facilitates," "fosters," and "promotes." These words all suggest that something is not being stopped, instead it is being facilitated or promoted. While "puts a stop to" has a negative connotation, its antonyms have a positive connotation and indicate progress, growth or development.