There are several ways for someone to enroll through Enrollsy and not pay:
Free Program
The first way is to set up a free Program by choosing the "Free" option under Pricing (in the Program settings).
Coupon
The second way is to provide your customer with a special Coupon that discounts the fee/tuition.
Admin Enroll
The third way is for an Admin User to enroll them. Admins can bypass pricing when enrolling someone on the backend.