In what cases do prosecutors agree to drop the charges before formal judicial proceedings begin, on the condition that suspects participate in and complete a program?

Diversion cases.

Explanation:

Diversion consists of implementing methodologies that seek to elude the usual processing a criminal justice system carries out on a lawbreaker. Even though those methodologies are shaped in many ways, a standard diversion program directs a lawbreaker to treatment or a care program as another possibility different from criminal accusation and imprisoning.